{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T01:48:03Z","timestamp":1773798483421,"version":"3.50.1"},"publisher-location":"Providence, Rhode Island","reference-count":56,"publisher":"American Mathematical Society","isbn-type":[{"value":"9781470410322","type":"print"},{"value":"9781470422646","type":"print"},{"value":"9781470422691","type":"print"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"abstract":"<p>\n                    This is a survey article on a question, posed in 1985 by M. Cohen, whether the smash product\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper A number-sign upper H\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>A<\/mml:mi>\n                            <mml:mi mathvariant=\"normal\">\n                              #\n                              \n                            <\/mml:mi>\n                            <mml:mi>H<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">A\\#H<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    of a semisimple Hopf algebra and a semiprime left\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H\">\n                        <mml:semantics>\n                          <mml:mi>H<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">H<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -module algebra\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper A\">\n                        <mml:semantics>\n                          <mml:mi>A<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">A<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is itself semiprime.\n                  <\/p>","DOI":"10.1090\/conm\/634\/12700","type":"other","created":{"date-parts":[[2015,2,26]],"date-time":"2015-02-26T10:14:53Z","timestamp":1424945693000},"page":"205-222","source":"Crossref","is-referenced-by-count":0,"title":["On the Semiprime Smash Product Question"],"prefix":"10.1090","author":[{"given":"Christian","family":"Lomp","sequence":"first","affiliation":[]}],"member":"14","reference":[{"key":"1","series-title":"Cambridge Tracts in Mathematics","isbn-type":"print","volume-title":"Hopf algebras","volume":"74","author":"Abe, Eiichi","year":"1980","ISBN":"https:\/\/id.crossref.org\/isbn\/0521222400"},{"issue":"2","key":"2","doi-asserted-by":"publisher","first-page":"634","DOI":"10.1006\/jabr.1997.7314","article-title":"Identities of algebras with actions of Hopf algebras","volume":"202","author":"Bahturin, Y. A.","year":"1998","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"issue":"1-2","key":"3","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/S0022-4049(00)00087-6","article-title":"On actions of Hopf algebras with cocommutative coradical","volume":"161","author":"Beidar, K. I.","year":"2001","journal-title":"J. Pure Appl. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0022-4049","issn-type":"print"},{"key":"4","isbn-type":"print","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1090\/conm\/043\/810641","article-title":"Everybody knows what a Hopf algebra is","author":"Bergman, George M.","year":"1985","ISBN":"https:\/\/id.crossref.org\/isbn\/0821850466"},{"key":"5","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1112\/plms\/s3-27.1.69","article-title":"Rings with fixed-point-free group actions","volume":"27","author":"Bergman, G. M.","year":"1973","journal-title":"Proc. London Math. Soc. (3)","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6115","issn-type":"print"},{"issue":"1","key":"6","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/0021-8693(85)90099-7","article-title":"A duality theorem for Hopf module algebras","volume":"95","author":"Blattner, Robert J.","year":"1985","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"issue":"4","key":"7","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1007\/BF01815526","article-title":"A coassociative \ud835\udc36*-quantum group with nonintegral dimensions","volume":"38","author":"B\u00f2hm, Gabriella","year":"1996","journal-title":"Lett. Math. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-9017","issn-type":"print"},{"key":"8","doi-asserted-by":"publisher","first-page":"Art. ID 546058, 9","DOI":"10.1155\/2011\/546058","article-title":"Quantum groupoids acting on semiprime algebras","author":"Borges, In\u00eas","year":"2011","journal-title":"Adv. Math. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/1687-9120","issn-type":"print"},{"key":"9","series-title":"London Mathematical Society Lecture Note Series","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511546495","volume-title":"Corings and comodules","volume":"309","author":"Brzezinski, Tomasz","year":"2003","ISBN":"https:\/\/id.crossref.org\/isbn\/0521539315"},{"key":"10","isbn-type":"print","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1090\/conm\/043\/810642","article-title":"Hopf algebras acting on semiprime algebras","author":"Cohen, Miriam","year":"1985","ISBN":"https:\/\/id.crossref.org\/isbn\/0821850466"},{"issue":"2","key":"11","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1016\/0021-8693(90)90274-R","article-title":"Hopf Galois extensions, smash products, and Morita equivalence","volume":"133","author":"Cohen, M.","year":"1990","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"issue":"1","key":"12","doi-asserted-by":"publisher","first-page":"237","DOI":"10.2307\/1999586","article-title":"Group-graded rings, smash products, and group actions","volume":"282","author":"Cohen, M.","year":"1984","journal-title":"Trans. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9947","issn-type":"print"},{"issue":"11","key":"13","doi-asserted-by":"publisher","first-page":"1253","DOI":"10.1080\/00927878308822904","article-title":"Group graded rings","volume":"11","author":"Cohen, Miriam","year":"1983","journal-title":"Comm. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0092-7872","issn-type":"print"},{"issue":"1","key":"14","doi-asserted-by":"publisher","first-page":"111","DOI":"10.17323\/1609-4514-2004-4-1-111-130","article-title":"Rankin-Cohen brackets and the Hopf algebra of transverse geometry","volume":"4","author":"Connes, Alain","year":"2004","journal-title":"Mosc. Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/1609-3321","issn-type":"print"},{"issue":"2","key":"15","doi-asserted-by":"publisher","first-page":"664","DOI":"10.1006\/jabr.1998.7568","article-title":"Semisimple Hopf algebras of dimension \ud835\udc5d\ud835\udc5e are trivial","volume":"210","author":"Etingof, Pavel","year":"1998","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"issue":"5","key":"16","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1155\/S1073792800000131","article-title":"The classification of triangular semisimple and cosemisimple Hopf algebras over an algebraically closed field","author":"Etingof, Pavel","year":"2000","journal-title":"Internat. Math. Res. Notices","ISSN":"https:\/\/id.crossref.org\/issn\/1073-7928","issn-type":"print"},{"key":"17","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.aim.2013.10.008","article-title":"Semisimple Hopf actions on commutative domains","volume":"251","author":"Etingof, Pavel","year":"2014","journal-title":"Adv. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0001-8708","issn-type":"print"},{"issue":"1","key":"18","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1016\/0021-8693(78)90272-7","article-title":"Semiprime skew group rings","volume":"52","author":"Fisher, Joe W.","year":"1978","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"issue":"6","key":"19","doi-asserted-by":"publisher","first-page":"943","DOI":"10.4310\/MRL.2007.v14.n6.a4","article-title":"Simple Hopf algebras and deformations of finite groups","volume":"14","author":"Galindo, C\u00e9sar","year":"2007","journal-title":"Math. Res. Lett.","ISSN":"https:\/\/id.crossref.org\/issn\/1073-2780","issn-type":"print"},{"key":"20","doi-asserted-by":"publisher","first-page":"360","DOI":"10.2969\/jmsj\/01840360","article-title":"On semisimple extensions and separable extensions over non commutative rings","volume":"18","author":"Hirata, Kazuhiko","year":"1966","journal-title":"J. Math. Soc. Japan","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5645","issn-type":"print"},{"key":"21","isbn-type":"print","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/978-3-7643-8742-6_16","article-title":"Pseudo-Galois extensions and Hopf algebroids","author":"Kadison, Lars","year":"2008","ISBN":"https:\/\/id.crossref.org\/isbn\/9783764387419"},{"key":"22","series-title":"Lecture Notes in Mathematics","volume-title":"Bialgebras","author":"Kaplansky, Irving","year":"1975"},{"issue":"10","key":"23","doi-asserted-by":"publisher","first-page":"3640","DOI":"10.1016\/j.jalgebra.2009.08.018","article-title":"Gorenstein subrings of invariants under Hopf algebra actions","volume":"322","author":"Kirkman, E.","year":"2009","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"key":"24","doi-asserted-by":"publisher","first-page":"75","DOI":"10.2307\/2373270","article-title":"An associative orthogonal bilinear form for Hopf algebras","volume":"91","author":"Larson, Richard Gustavus","year":"1969","journal-title":"Amer. J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9327","issn-type":"print"},{"issue":"1","key":"25","doi-asserted-by":"publisher","first-page":"187","DOI":"10.2307\/2374545","article-title":"Semisimple cosemisimple Hopf algebras","volume":"110","author":"Larson, Richard G.","year":"1988","journal-title":"Amer. J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9327","issn-type":"print"},{"key":"26","isbn-type":"print","first-page":"121","article-title":"Nilpotent subsets of Hopf module algebras","author":"Linchenko, V.","year":"2003","ISBN":"https:\/\/id.crossref.org\/isbn\/1402012209"},{"issue":"10","key":"27","doi-asserted-by":"publisher","first-page":"3091","DOI":"10.1090\/S0002-9939-07-08849-1","article-title":"Semiprime smash products and \ud835\udc3b-stable prime radicals for PI-algebras","volume":"135","author":"Linchenko, V.","year":"2007","journal-title":"Proc. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9939","issn-type":"print"},{"key":"28","volume-title":"Primeigenschaften von Algebren in Modulkategorien \\\"uber Hopfalgebren","author":"Lomp, C.","year":"2002"},{"issue":"1","key":"29","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1016\/j.jalgebra.2003.07.017","article-title":"When is a smash product semiprime? A partial answer","volume":"275","author":"Lomp, Christian","year":"2004","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"issue":"12","key":"30","doi-asserted-by":"publisher","first-page":"4687","DOI":"10.1081\/AGB-200036837","article-title":"Integrals in Hopf algebras over rings","volume":"32","author":"Lomp, Christian","year":"2004","journal-title":"Comm. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0092-7872","issn-type":"print"},{"issue":"1-3","key":"31","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1016\/j.jpaa.2004.10.009","article-title":"A central closure construction for certain algebra extensions. Applications to Hopf actions","volume":"198","author":"Lomp, Christian","year":"2005","journal-title":"J. Pure Appl. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0022-4049","issn-type":"print"},{"issue":"1","key":"32","first-page":"137","article-title":"A note on extending Hopf actions to rings of quotients of module algebras","volume":"47","author":"Lomp, Christian","year":"2006","journal-title":"Beitr\\\"{a}ge Algebra Geom.","ISSN":"https:\/\/id.crossref.org\/issn\/0138-4821","issn-type":"print"},{"issue":"19","key":"33","doi-asserted-by":"publisher","first-page":"1853","DOI":"10.1080\/00927878008822549","article-title":"Two applications of Maschke\u2019s theorem","volume":"8","author":"Lorenz, Martin","year":"1980","journal-title":"Comm. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0092-7872","issn-type":"print"},{"issue":"1","key":"34","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/S0393-0440(96)00022-8","article-title":"Quasi-* structure on \ud835\udc5e-Poincar\u00e9 algebras","volume":"22","author":"Majid, S.","year":"1997","journal-title":"J. Geom. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0393-0440","issn-type":"print"},{"issue":"1-3","key":"35","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1007\/BF02762089","article-title":"Semisimple Hopf algebras of dimension 6,8","volume":"92","author":"Masuoka, Akira","year":"1995","journal-title":"Israel J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-2172","issn-type":"print"},{"issue":"3","key":"36","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1090\/S0002-9939-96-03147-4","article-title":"The \ud835\udc5d\u207f theorem for semisimple Hopf algebras","volume":"124","author":"Masuoka, Akira","year":"1996","journal-title":"Proc. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9939","issn-type":"print"},{"issue":"7","key":"37","doi-asserted-by":"publisher","first-page":"1909","DOI":"10.1080\/00927879108824237","article-title":"Centrally closed Hopf module algebras","volume":"19","author":"Matczuk, Jerzy","year":"1991","journal-title":"Comm. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0092-7872","issn-type":"print"},{"key":"38","series-title":"CBMS Regional Conference Series in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1090\/cbms\/082","volume-title":"Hopf algebras and their actions on rings","volume":"82","author":"Montgomery, Susan","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/0821807382"},{"issue":"1-2","key":"39","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/BF02764636","article-title":"Biinvertible actions of Hopf algebras.","volume":"83","author":"Montgomery, S.","year":"1993","journal-title":"{Isr. J. Math.}"},{"key":"40","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/BF02773482","article-title":"Prime ideals in Hopf Galois extensions","volume":"112","author":"Montgomery, S.","year":"1999","journal-title":"Israel J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-2172","issn-type":"print"},{"issue":"3","key":"41","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/S0022-4049(97)00077-7","article-title":"Irreducible representations of crossed products","volume":"129","author":"Montgomery, Susan","year":"1998","journal-title":"J. Pure Appl. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0022-4049","issn-type":"print"},{"issue":"874","key":"42","doi-asserted-by":"publisher","first-page":"viii+123","DOI":"10.1090\/memo\/0874","article-title":"Semisolvability of semisimple Hopf algebras of low dimension","volume":"186","author":"Natale, Sonia","year":"2007","journal-title":"Mem. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-9266","issn-type":"print"},{"key":"43","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1080\/00927879808826132","article-title":"\ud835\udc3e\u2080-rings and twistings of finite dimensional semisimple Hopf algebras","volume":"26","author":"Nikshych, D.","year":"1998","journal-title":"Comm. Alg."},{"key":"44","isbn-type":"print","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1090\/conm\/130\/1176129","article-title":"A Connes spectrum for Hopf algebras","author":"Osterburg, James","year":"1992","ISBN":"https:\/\/id.crossref.org\/isbn\/082185142X"},{"issue":"5-6","key":"45","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1007\/s10485-006-9052-5","article-title":"Some bialgebroids constructed by Kadison and Connes-Moscovici are isomorphic","volume":"14","author":"Panaite, Florin","year":"2006","journal-title":"Appl. Categ. Structures","ISSN":"https:\/\/id.crossref.org\/issn\/0927-2852","issn-type":"print"},{"key":"46","doi-asserted-by":"publisher","first-page":"588","DOI":"10.1016\/0021-8693(71)90141-4","article-title":"When Hopf algebras are Frobenius algebras","volume":"18","author":"Pareigis, Bodo","year":"1971","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"key":"47","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1007\/BF02261710","article-title":"Maximal Quotient Algebra of a Hopf-Module Algebra","volume":"32","author":"Rumynin, D.","year":"1993","journal-title":"Algebra and Logic"},{"key":"48","series-title":"Trabajos de Matem\\'{a}tica [Mathematical Works]","volume-title":"Lectures on Hopf algebras","volume":"31\/95","author":"Schneider, Hans-J\u00fcrgen","year":"1995"},{"key":"49","volume-title":"Study of torsion theories of Hopf module algebras and their smash products","author":"Selvan, V.","year":"1994"},{"issue":"2","key":"50","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1007\/BF02367372","article-title":"Globalization of local actions of coalgebras","volume":"35","author":"Sidorov, A. V.","year":"1996","journal-title":"Algebra i Logika","ISSN":"https:\/\/id.crossref.org\/issn\/0373-9252","issn-type":"print"},{"issue":"1","key":"51","doi-asserted-by":"publisher","first-page":"292","DOI":"10.1016\/j.jalgebra.2006.06.030","article-title":"The Goldie Theorem for \ud835\udc3b-semiprime algebras","volume":"305","author":"Skryabin, Serge","year":"2006","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"key":"52","series-title":"Mathematics Lecture Note Series","volume-title":"Hopf algebras","author":"Sweedler, Moss E.","year":"1969"},{"key":"53","doi-asserted-by":"publisher","first-page":"323","DOI":"10.2307\/1970672","article-title":"Integrals for Hopf algebras","volume":"89","author":"Sweedler, Moss Eisenberg","year":"1969","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"issue":"14","key":"54","doi-asserted-by":"publisher","first-page":"1455","DOI":"10.1080\/00927878108822655","article-title":"Localization of modules on the central closure of rings","volume":"9","author":"Wisbauer, Robert","year":"1981","journal-title":"Comm. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0092-7872","issn-type":"print"},{"key":"55","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1155\/S1073792894000073","article-title":"Hopf algebras of prime dimension","volume":"1","author":"Zhu, Y.","year":"1994","journal-title":"Inter. Math. Research Not."},{"issue":"1","key":"56","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1006\/jabr.1996.0060","article-title":"Integrality of module algebras over its invariants","volume":"180","author":"Zhu, Shenglin","year":"1996","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"}],"container-title":["Contemporary Mathematics","Noncommutative Rings and Their Applications"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T22:19:04Z","timestamp":1773785944000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/conm\/634\/12700\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9781470410322","9781470422646","9781470422691"],"references-count":56,"URL":"https:\/\/doi.org\/10.1090\/conm\/634\/12700","relation":{},"ISSN":["0271-4132","1098-3627"],"issn-type":[{"value":"0271-4132","type":"print"},{"value":"1098-3627","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]}}}