{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:39:20Z","timestamp":1774625960471,"version":"3.50.1"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2005,1,1]],"date-time":"2005-01-01T00:00:00Z","timestamp":1104537600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2005,1,1]],"date-time":"2005-01-01T00:00:00Z","timestamp":1104537600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann. Univ. Ferrara"],"published-print":{"date-parts":[[2005,1]]},"DOI":"10.1007\/bf02824832","type":"journal-article","created":{"date-parts":[[2022,1,24]],"date-time":"2022-01-24T18:30:38Z","timestamp":1643049038000},"page":"209-231","source":"Crossref","is-referenced-by-count":10,"title":["Galois theory for bialgebroids, depth two and normal Hopf subalgebras"],"prefix":"10.1007","volume":"51","author":[{"given":"Lars","family":"Kadison","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"BF02824832_CR1","unstructured":"I. B\u00e1lint\u2014K. Szlach\u00e1nyi,Finitary Galois extensions over non-commutative bases, KFKI preprint (2004), RA\/0412122."},{"key":"BF02824832_CR2","unstructured":"T. Brzezi\u0144ski\u2014R.B. Turner\u2014A.P. Wrightson,The structure of weak coalgebra-Galois extensions, preprint (2004), QA\/0411230."},{"key":"BF02824832_CR3","doi-asserted-by":"crossref","unstructured":"T. Brezezi\u0144ski\u2014R. Wisbauer,Corings and Comodules, LMS,309, Cambridge University Press, 2003.","DOI":"10.1017\/CBO9780511546495"},{"key":"BF02824832_CR4","unstructured":"G. B\u00f6hm,Galois theory for Hopf algebroids, KFKI preprint (2004), RA\/0409513."},{"key":"BF02824832_CR5","doi-asserted-by":"publisher","first-page":"708","DOI":"10.1016\/j.jalgebra.2003.09.005","volume":"274","author":"G. B\u00f6hm","year":"2004","unstructured":"G. B\u00f6hm\u2014K. Szlach\u00e1nyi,Hopf algebroids with bijective antipodes: axioms, integrals and duals, J. Algebra,274 (2004), pp. 708\u2013750.","journal-title":"J. Algebra"},{"key":"BF02824832_CR6","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1006\/jabr.1999.7984","volume":"221","author":"G. B\u00f6hm","year":"1999","unstructured":"G. B\u00f6hm\u2014F. Nill\u2014K. Szlach\u00e1nyi,Weak Hopf algebras, I. Integral theory and C\n                  *-structure, J. Algebra221 (1999), pp. 385\u2013438.","journal-title":"J. Algebra"},{"key":"BF02824832_CR7","unstructured":"S. Caenepeel\u2014E. De Groot,Galois theory for weak Hopf algebras, preprint (2004), RA\/0406186."},{"key":"BF02824832_CR8","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1215\/S0012-7094-01-10814-4","volume":"108","author":"P. Etingof","year":"2001","unstructured":"P. Etingof\u2014D. Nikshych,Dynamical quantum groups at roots of\n                  1 Duke Math. J.,108 (2001), pp. 135\u2013168.","journal-title":"Duke Math. J."},{"key":"BF02824832_CR9","doi-asserted-by":"publisher","first-page":"4857","DOI":"10.1090\/S0002-9947-97-01814-X","volume":"349","author":"D. Fischman","year":"1997","unstructured":"D. Fischman\u2014S. Montgomery\u2014H.-J. Schneider,Frobenius extensions of subalgebras of Hopf algebras, Trans. Amer. Math. Soc.349 (1997), pp. 4857\u20134895.","journal-title":"Trans. Amer. Math. Soc."},{"key":"BF02824832_CR10","series-title":"University Lecture Series","doi-asserted-by":"crossref","DOI":"10.1090\/ulect\/014","volume-title":"New Examples of Frobenius Extensions","author":"L. Kadison","year":"1999","unstructured":"L. Kadison,New Examples of Frobenius Extensions, University Lecture Series14, AMS, Providence, 1999. Update, 6 pp. www.ams.org\/bookpages."},{"key":"BF02824832_CR11","unstructured":"L. Kadison,Depth two and the Galois coring, in: Noncommutative geometry and representation theory in mathematical physics, ed. J. Fuchs, AMS Contemporary Math, to appear. RA\/0408155."},{"key":"BF02824832_CR12","unstructured":"L. Kadison,An action-free characterization of weak Hopf-Galois extensions Algebra Montpellier Announcements (2005), 1\u20136."},{"key":"BF02824832_CR13","unstructured":"L. Kadison,Normal Hopf subalgebras, depth two and Galois extensions, preprint (2004), QA\/0411129."},{"key":"BF02824832_CR14","unstructured":"L. Kadison\u2014B. K\u00fclshammer,Depth two, normality and a trace ideal condition for Frobenius extensions, Comm. Algebra, to appear. GR\/0409346."},{"key":"BF02824832_CR15","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1006\/aima.2001.2003","volume":"163","author":"L. Kadison","year":"2001","unstructured":"L. Kadison\u2014D. Nikshych,Hopf algebra actions on strongly separable extensions of depth two, Adv. in Math.,163 (2001), pp. 258\u2013286","journal-title":"Adv. in Math."},{"key":"BF02824832_CR16","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/S0001-8708(02)00028-2","volume":"179","author":"L. Kadison","year":"2003","unstructured":"L. Kadison\u2014K. Szlach\u00e1nyi,Bialgebroid actions on depth two extensions and duality, Adv. in Math.,179 (2003), pp. 75\u2013121: RA\/0108067.","journal-title":"Adv. in Math."},{"key":"BF02824832_CR17","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1142\/S0129167X96000050","volume":"7","author":"J.-H. Lu","year":"1996","unstructured":"J.-H. Lu,Hopf algebroids and quantum groupoids, Int. J. Math.,7 (1996), pp. 47\u201370.","journal-title":"Int. J. Math."},{"key":"BF02824832_CR18","doi-asserted-by":"crossref","unstructured":"S. Majid,Foundations of Quantum Group Theory, Cambridge Univ. Press, 1995.","DOI":"10.1017\/CBO9780511613104"},{"key":"BF02824832_CR19","series-title":"CBMS Regional Conf. Series in Math.","doi-asserted-by":"crossref","DOI":"10.1090\/cbms\/082","volume-title":"Hopf Algebras and Their Actions on Rings","author":"S. Montgomery","year":"1993","unstructured":"S. Montgomery,Hopf Algebras and Their Actions on Rings, CBMS Regional Conf. Series in Math., Vol.82, AMS, Providence, 1993."},{"key":"BF02824832_CR20","unstructured":"D. Nikshych\u2014L. Vainerman,Finite dimensional quantum groupoids and their applications, in: New Directions in Hopf Algebras, S. Montgomery and H.-J. Schneider, eds., MSRI Publications, vol.43, Cambridge, 2002, pp. 211\u2013262."},{"key":"BF02824832_CR21","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1090\/S0002-9939-97-03682-4","volume":"125","author":"P. Schauenburg","year":"1997","unstructured":"P. Schauenburg,A bialgebra that admits a Hopf-Galois extension is a Hopf algebra, Proc. A.M.S.125 (1997), pp. 83\u201385.","journal-title":"Proc. A.M.S."},{"key":"BF02824832_CR22","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1016\/0021-8693(92)90034-J","volume":"151","author":"H.-J. Schneider","year":"1992","unstructured":"H.-J. Schneider,Normal basis and transitivity of crossed products for Hopf algebras, J. Algebra,151 (1992), pp. 289\u2013312.","journal-title":"J. Algebra"},{"key":"BF02824832_CR23","series-title":"IRMA Lect. Math. Phys.","first-page":"105","volume-title":"Galois actions by finite quantum groupoids, Locally compact quantum groups and groupoids (Strasbourg, 2002)","author":"K. Szlach\u00e1nyi","year":"2003","unstructured":"K. Szlach\u00e1nyi,Galois actions by finite quantum groupoids, Locally compact quantum groups and groupoids (Strasbourg, 2002), IRMA Lect. Math. Phys. 2, de Gruyter, (Berlin, 2003), pp. 105\u2013125. QA\/0205229."},{"key":"BF02824832_CR24","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1016\/j.jalgebra.2003.02.001","volume":"270","author":"P. Vecserny\u00e9s","year":"2003","unstructured":"P. Vecserny\u00e9s,Larson-Sweedler theorem and the role of grouplike elements in weak Hopf algebras, J. Algebra,270 (2003), pp. 471\u2013520.","journal-title":"J. Algebra"}],"container-title":["ANNALI DELL UNIVERSITA DI FERRARA"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02824832.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/BF02824832\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02824832.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,24]],"date-time":"2022-01-24T18:30:42Z","timestamp":1643049042000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/BF02824832"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,1]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2005,1]]}},"alternative-id":["BF02824832"],"URL":"https:\/\/doi.org\/10.1007\/bf02824832","relation":{},"ISSN":["0430-3202","1827-1510"],"issn-type":[{"value":"0430-3202","type":"print"},{"value":"1827-1510","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,1]]}}}