{"id":2272,"date":"2024-06-29T11:39:13","date_gmt":"2024-06-29T11:39:13","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2272"},"modified":"2024-06-30T00:13:17","modified_gmt":"2024-06-30T00:13:17","slug":"on-residually-completely-integrally-closed-rings","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/on-residually-completely-integrally-closed-rings\/","title":{"rendered":"On Residually (Completely) Integrally Closed Rings"},"content":{"rendered":"\n<div style=\"height:63px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:25%\">\n<figure class=\"wp-block-image size-full is-resized is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"468\" height=\"577\" src=\"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-content\/uploads\/2022\/03\/logovf-4.png\" alt=\"\" class=\"wp-image-752\" style=\"width:150px;height:200px\" srcset=\"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-content\/uploads\/2022\/03\/logovf-4.png 468w, https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-content\/uploads\/2022\/03\/logovf-4-243x300.png 243w\" sizes=\"auto, (max-width: 468px) 100vw, 468px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:70%\">\n<p style=\"font-size:21px\"><strong>Moroccan Journal of Algebra and Geometry with Applications<\/strong><\/p>\n\n\n\n<p><a href=\"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/latest-issue\/\" data-type=\"link\" data-id=\"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/latest-issue\/\">Latest articles<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:1200px\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<p class=\"has-text-align-center has-text-color has-huge-font-size\" style=\"color:#060182\"><strong>On Residually (Completely) Integrally Closed Rings<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-align-center\" style=\"font-size:18.5px\"><strong>Ali Tamoussit&nbsp;<\/strong><i class=\"fas fa-envelope\"><\/i><br>  Department of Mathematics, The Regional Center for Education and Training Professions Souss <br>  Massa, Inezgane, Morocco.<\/p>\n\n\n\n<div style=\"height:35px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-center has-text-color\" style=\"color:#232222;font-size:16px\"><span style=\"color:#626161\" class=\"color\">Pages 187-196 |  Received 09 November 2023,  Accepted 11 January 2024, Published 30 June 2024  <\/span><\/p>\n\n\n\n<div style=\"height:31px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:25%\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:250%\">\n<div style=\"height:51px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-large-font-size\"><strong><span style=\"color:#060182\" class=\"color\">Abstract<\/span><\/strong><\/p>\n\n\n\n<p>All rings considered in this paper are commutative rings with identity. A ring <span class=\"katex-eq\" data-katex-display=\"false\">R<\/span> is called a residually completely<br>integrally closed (for short, <span class=\"katex-eq\" data-katex-display=\"false\">RCIC<\/span>) ring if the integral domain <span class=\"katex-eq\" data-katex-display=\"false\">R\/P<\/span> is completely integrally closed, for all prime ideals <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span> of <span class=\"katex-eq\" data-katex-display=\"false\">R<\/span>. The main goal of this paper is to study the behavior of the <span class=\"katex-eq\" data-katex-display=\"false\">RCIC<\/span> property in some distinguished constructions such as homomorphic image, finite direct products, Nagata ring, amalgamated duplications of rings and trivial ring extensions. Our study is then extended to the case of residually integrally closed rings.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-small-font-size\"><span style=\"color:#060182\" class=\"color\"><strong>Keywords<\/strong>:<\/span>&nbsp; (Completely) integrally closed, Nagata ring, amalgamated duplication, trivial ring extension.<\/p>\n\n\n\n<p class=\"has-small-font-size\"><span style=\"color:#060182\" class=\"color\"><strong>MSC numbers<\/strong>:<\/span> Primary 13A15, 13B22; Secondary 13B02, 13F99.<\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>Downloads:<\/strong> <a href=\"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-content\/uploads\/2024\/06\/MJAGA_Vol3_Iss1_9_187_196_Bis.pdf\" data-type=\"link\" data-id=\"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-content\/uploads\/2024\/06\/MJAGA_Vol3_Iss1_9_187_196_Bis.pdf\">Full-text PDF<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:25%\"><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:25%\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:800px\"><a href=\"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-content\/uploads\/2024\/06\/MJAGA_Vol3_Iss1_9_187_196_Bis.pdf\" class=\"pdfemb-viewer\" style=\"width:700px;height:950px;\" data-width=\"700\" data-height=\"950\" data-toolbar=\"bottom\" data-toolbar-fixed=\"off\">MJAGA_Vol3_Iss1_9_187_196_Bis<\/a><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:25%\"><\/div>\n<\/div>\n\n\n\n<div style=\"height:96px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-buttons is-content-justification-right is-layout-flex wp-container-core-buttons-is-layout-765c4724 wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-outline is-style-outline--1\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/on-phi-prufer-and-phi-bezout-rings-in-amalgamation-algebra-along-an-ideal\/\" style=\"border-radius:100px\">Previous article <\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-outline is-style-outline--2\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/moroccan-journal-of-algebra-and-geometry-with-applications-volume-3-issue-1-2024\/\" style=\"border-radius:100px\"><strong>View<\/strong>&nbsp;issue table of contents<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-buttons is-content-justification-left is-layout-flex wp-container-core-buttons-is-layout-fdcfc74e wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-outline is-style-outline--3\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/fast-multiplication-algorithm-for-square-sparse-matrices-application-to-images-processing\/\" style=\"border-radius:100px\"><strong>Next<\/strong>&nbsp;article<\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Moroccan Journal of Algebra and Geometry with Applications Latest articles On Residually (Completely) Integrally Closed Rings Ali Tamoussit&nbsp; Department of Mathematics, The Regional Center for Education and Training Professions Souss Massa, Inezgane, Morocco. Pages 187-196 | Received 09 November 2023, Accepted 11 January 2024, Published 30 June 2024 Abstract All rings considered in this paper <a class=\"read-more-link\" href=\"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/on-residually-completely-integrally-closed-rings\/\">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-2272","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2272","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=2272"}],"version-history":[{"count":3,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2272\/revisions"}],"predecessor-version":[{"id":2321,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2272\/revisions\/2321"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2272"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}