{"id":1731,"date":"2023-06-14T13:51:51","date_gmt":"2023-06-14T13:51:51","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=1731"},"modified":"2023-10-12T22:04:43","modified_gmt":"2023-10-12T22:04:43","slug":"note-on-bi-amalgamated-modules-along-ideals","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/note-on-bi-amalgamated-modules-along-ideals\/","title":{"rendered":"Note on bi-Amalgamated modules along ideals"},"content":{"rendered":"\n
<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n\n
\n

Moroccan Journal of Algebra and Geometry with Applications<\/strong><\/p>\n\n\n\n

Latest articles<\/a><\/p>\n<\/div>\n\n\n\n

\n
<\/div>\n<\/div>\n\n\n\n
<\/div>\n\n\n\n
<\/div>\n<\/div>\n\n\n\n
\n
\n

Note on bi-Amalgamated modules along ideals<\/em><\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

Adam Anebri <\/strong><\/i>
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.<\/p>\n\n\n\n

<\/div>\n\n\n\n

Pages 83-92 | Received 20 November 2022, Accepted 20 January 2023, Published 16 June 2023 <\/span><\/p>\n\n\n\n

<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n

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

Let f: A\\rightarrow B<\/span> and g: A\\rightarrow C<\/span> be two commutative ring homomorphisms and let J<\/span> and J'<\/span> be two ideals of B<\/span> and C<\/span>, respectively, such that f^{-1}(J)=g^{-1}(J')<\/span>. The bi-amalgamation of <\/span> with (B, C)<\/span> along (J, J')<\/span> with respect to (f,g)<\/span>, denoted by A\\bowtie^{f,g}(J,J')<\/span>, is the subring of B\\times C<\/span> given by A\\bowtie^{f,g}(J,J'):= \\{(f(a)+j,g(a)+j') \\mid a\\in A, (j,j')\\in J\\times J'\\}.<\/span> In this paper, we study some basic properties of a special kind of A\\bowtie^{f,g}(J,J')<\/span>-modules,called the bi-amalgamation of M<\/span> with (N,P)<\/span> along (J,J')<\/span> with respect (\\varphi,\\psi)<\/span>, and defined by M \\bowtie^{\\varphi,\\psi}(JN,J'P) := \\{(\\varphi(m)+n,\\psi(m) + p)\\ |\\ m\\in M \\text{ and } (n,p) \\in JN\\times J'P\\}<\/span>. The new results generalize some known results on the bi-amalgamation of rings and the amalgamation of modules along an ideal. <\/p>\n\n\n\n

Keywords<\/strong>:<\/span>  Bi-amalgamation, amalgamation, Noetherian module, prime module, reduced module, coherent module. <\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> 13E05, 13D05, 13D02, 13C60.<\/p>\n\n\n\n

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

<\/div>\n<\/div>\n\n\n\n
\n
<\/div>\n\n\n\n
0201MJAGA83_92<\/a>\n

<\/p>\n<\/div>\n\n\n\n

<\/div>\n<\/div>\n\n\n\n
<\/div>\n\n\n\n
\n
\n
\n
Previous article <\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n
\n
\n
View<\/strong> issue table of contents<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n
\n
\n
Next<\/strong> article<\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Moroccan Journal of Algebra and Geometry with Applications Latest articles Note on bi-Amalgamated modules along ideals Adam Anebri  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. Pages 83-92 | Received 20 November 2022, Accepted 20 January 2023, Published 16 June 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-1731","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1731","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=1731"}],"version-history":[{"count":12,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1731\/revisions"}],"predecessor-version":[{"id":1938,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1731\/revisions\/1938"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=1731"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}