{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T08:30:12Z","timestamp":1767861012917,"version":"3.49.0"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2015,8]]},"abstract":"<jats:p> Let R be a ring, and let S be a strictly ordered monoid. The generalized power series ring R[[S]] is a common generalization of polynomial rings, Laurent polynomial rings, power series rings, Laurent series rings, Mal'cev\u2013Neumann series rings, monoid rings and group rings. In this paper, we examine which conditions on R and S are necessary and which are sufficient for the generalized power series ring R[[S]] to be semilocal right B\u00e9zout or semilocal right distributive. In the case where S is a strictly totally ordered monoid we characterize generalized power series rings R[[S]] that are semilocal right distributive or semilocal right B\u00e9zout (the latter under the additional assumption that S is not a group). <\/jats:p>","DOI":"10.1142\/s0218196715500174","type":"journal-article","created":{"date-parts":[[2015,4,8]],"date-time":"2015-04-08T04:43:27Z","timestamp":1428468207000},"page":"725-744","source":"Crossref","is-referenced-by-count":4,"title":["On semilocal, B\u00e9zout and distributive generalized power series rings"],"prefix":"10.1142","volume":"25","author":[{"given":"Ryszard","family":"Mazurek","sequence":"first","affiliation":[{"name":"Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15\u2013351 Bia\u0142ystok, Poland"}]},{"given":"Micha\u0142","family":"Ziembowski","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00\u2013662 Warsaw, Poland"}]}],"member":"219","published-online":{"date-parts":[[2015,8,13]]},"reference":[{"key":"rf1","series-title":"Schriftenreihe des Fachbereichs Mathematics","volume-title":"Right Chain Rings","volume":"181","author":"Bessenrodt C.","year":"1990"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1002\/mana.19961820105"},{"key":"rf3","series-title":"Mathematical Surveys and Monographs","volume-title":"Rings and Things and a Fine Array of Twentieth Century Associative Algebra","volume":"65","author":"Faith C.","year":"1999"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2005.07.019"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-8693(03)00418-6"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0406-7"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-2436-4"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2006.07.030"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2007.08.024"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1080\/00927870801941150"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/06241093"},{"key":"rf12","first-page":"377","volume":"43","author":"Miyamoto H.","year":"1996","journal-title":"Math. Japon."},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02571375"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.2307\/2043421"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1017\/S0017089500005401"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1997.7063"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-28.2.291"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-5086-6"},{"key":"rf19","first-page":"913","volume":"6","author":"Tuganbaev D. A.","year":"2000","journal-title":"Fundam. Prikl. Mat."},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(75)90074-5"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1080\/00927877908822361"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-08-09577-4"},{"key":"rf24","first-page":"139","volume":"5","author":"Zhuchin A. V.","year":"1999","journal-title":"Fundam. Prikl. Mat."},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2012.720324"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196715500174","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T13:10:11Z","timestamp":1565097011000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196715500174"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8]]},"references-count":24,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2015,8,13]]},"published-print":{"date-parts":[[2015,8]]}},"alternative-id":["10.1142\/S0218196715500174"],"URL":"https:\/\/doi.org\/10.1142\/s0218196715500174","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,8]]}}}