{"id":830,"date":"2022-03-27T10:42:00","date_gmt":"2022-03-27T10:42:00","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=830"},"modified":"2022-07-04T11:10:03","modified_gmt":"2022-07-04T11:10:03","slug":"on-constructing-angles-with-prescribed-vertex-and-measure-in-the-upper-half-plane-model-of-hyperbolic-geometry","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/on-constructing-angles-with-prescribed-vertex-and-measure-in-the-upper-half-plane-model-of-hyperbolic-geometry\/","title":{"rendered":"On the category of algebras over a finite direct product of commutative rings"},"content":{"rendered":"\n
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Moroccan Journal of Algebra and Geometry with Applications<\/strong><\/p>\n\n\n\n

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On the category of algebras over a finite direct product of
<\/em><\/strong>commutative rings <\/em><\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

David E. Dobbs <\/strong><\/i>
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1320, USA<\/p>\n\n\n\n

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Pages 62-75 | Received 20 April 2021, Accepted 12 June 2021, Published 01 June<\/span> 2022 <\/span><\/p>\n\n\n\n

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Abstract<\/span><\/strong><\/p>\n\n\n\n

A full statement and a rather detailed proof are given of a folklore result describing the category of (unital) algebras over a finite direct product of commutative rings. Following an extensive survey of some recent work on minimal ring extensions and chain conditions for (unital) ring extensions such as the FCP and FMC properties, including generalizations of these conditions and the FIP property to ring extensions involving noncommutative rings, a corollary of the folklore theorem for FIP, FCP and FMC is given for ring extensions
A \\subseteq B<\/span> where A is a finite direct product of commutative rings and B is a (not necessarily commutative) A-algebra.<\/p>\n\n\n\n

Keywords<\/strong>:<\/span>  Commutative ring, unital algebra, finite direct product, categorical equivalence, minimal ringextension, FMC, FCP, FIP. <\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> Primary 16B50; Secondary 13B99, 18A05. <\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles On the category of algebras over a finite direct product of commutative rings David E. Dobbs  Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1320, USA Pages 62-75 | Received 20 April 2021, Accepted 12 June 2021, Published 01 June 2022 Abstract A full statement Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-page-builder.php","meta":{"footnotes":""},"class_list":["post-830","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/830","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/comments?post=830"}],"version-history":[{"count":20,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/830\/revisions"}],"predecessor-version":[{"id":1115,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/830\/revisions\/1115"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=830"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}