{"id":936,"date":"2022-03-29T13:48:24","date_gmt":"2022-03-29T13:48:24","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=936"},"modified":"2022-07-04T11:15:39","modified_gmt":"2022-07-04T11:15:39","slug":"amalgamation-extension-in-commutative-ring-theory-a-survey","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/amalgamation-extension-in-commutative-ring-theory-a-survey\/","title":{"rendered":"Amalgamation extension in commutative ring theory: a survey"},"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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Amalgamation extension in commutative ring theory: a survey<\/strong><\/em><\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n

Abdelhaq El Khalfi, Hwankoo Kim<\/strong> <\/i> & Najib Mahdou <\/strong>
Department oLaboratory of Topology, Algebra, Geometry and Discrete Mathematics, Faculty of <\/strong>
Sciences Ain Chock, Hassan II University of Casablanca, Morocco;
Hoseo University, Asan 31499, Republic of Korea;
Laboratory of Modelling and Mathematical Structures. Department of Mathematics, Faculty of
Science and Technology of Fez, Box 2202, University S. M. Ben Abdellah Fez, Morocco. <\/strong>
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Pages 139-182 | Received 30 November<\/span><\/span> 2021, Accepted 07 February 2022, Published 01 June<\/span><\/span><\/span><\/span><\/span> 2022 <\/span><\/p>\n\n\n\n

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

Let A<\/span> and B<\/span> be two rings, let J<\/span> be an ideal of B<\/span> and let f : A \\longrightarrow B<\/span> be a ring homomorphism. In this setting, we can consider the following subring of A \\times B<\/span>: <\/p>\n\n\n\n

A \\bowtie^{f} J = \\{(a, f(a) + j)\\mid a \\in A, j \\in J\\} <\/span><\/p>\n\n\n\n

called the amalgamation of A<\/span> with B<\/span> along J<\/span> with respect to f<\/span> (introduced and studied by D’Anna, Finocchiaro, and Fontana). This construction is a generalization of the amalgamated duplication of a ring along an ideal (introduced and studied by D’Anna and Fontana and denoted by A\\bowtie I<\/span>). In this paper, we survey known results concerning A \\bowtie^{f} J<\/span>.<\/p>\n\n\n\n

Keywords<\/strong>:<\/span>  amalgamated duplication, amalgamation of ring, pullback, trivial ring extension. <\/p>\n\n\n\n

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

Downloads:<\/strong> Full-text PDF<\/a> <\/p>\n<\/div>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles Amalgamation extension in commutative ring theory: a survey Abdelhaq El Khalfi, Hwankoo Kim & Najib Mahdou Department oLaboratory of Topology, Algebra, Geometry and Discrete Mathematics, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, Morocco; Hoseo University, Asan 31499, Republic of Korea; Laboratory of 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-936","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/936","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=936"}],"version-history":[{"count":26,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/936\/revisions"}],"predecessor-version":[{"id":1122,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/936\/revisions\/1122"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=936"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}