{"id":2021,"date":"2023-12-08T19:34:07","date_gmt":"2023-12-08T19:34:07","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2021"},"modified":"2023-12-11T13:38:54","modified_gmt":"2023-12-11T13:38:54","slug":"on-purity-with-respect-to-modules-of-flat-dimension-at-most-one","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/on-purity-with-respect-to-modules-of-flat-dimension-at-most-one\/","title":{"rendered":"On purity with respect to modules of flat dimension at most one"},"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 purity with respect to modules of flat dimension at most one <\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-align-center\" style=\"font-size:18.5px\"><strong>Mouhssine El-arabi <\/strong> <i class=\"fas fa-envelope\"><\/i> and Youssef Najem<br> Department of Mathematics, Moulay Ismail University, 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 291\u2013297 |  <span style=\"color:#626161\" class=\"color\"> Received 28 April 2023,  <\/span><\/span><span style=\"\" class=\"color\"><span style=\"color: rgb(98, 97, 97);\" class=\"color\"> Accepted<\/span><\/span><span style=\"color:#626161\" class=\"color\"><span style=\"color:#626161\" class=\"color\"> 08 September 2023, Published 11 December 2023  <\/span>  <\/span><\/p>\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>The main goal of this paper is to extend the results of D. Benson and G. Gnacadja on pure homological algebra<br>in [1] to purity with respect to modules of flat dimension at most one.<\/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; global dimension; pure injective module; pure projective module; Auslander-Bridger transpose.           <\/p>\n\n\n\n<p class=\"has-small-font-size\"><span style=\"color:#060182\" class=\"color\"><strong>MSC numbers<\/strong>:<\/span> 18G25.<\/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\/2023\/12\/MJAGA_Vol2_Issue2-291-297.pdf\" data-type=\"link\" data-id=\"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-content\/uploads\/2023\/12\/MJAGA_Vol2_Issue2-272-290.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\/2023\/12\/MJAGA_Vol2_Issue2-291-297.pdf\" class=\"pdfemb-viewer\" style=\"width:700px;height:950px;\" data-width=\"700\" data-height=\"950\" data-toolbar=\"bottom\" data-toolbar-fixed=\"off\">MJAGA_Vol2_Issue2-291-297<\/a>\n<p class=\"wp-block-pdfemb-pdf-embedder-viewer\"><\/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 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-the-nature-and-number-of-the-noncommutative-minimal-ring-extensions-of-a-field\/\" 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-2-issue-2-2023\/\" 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\/semireversibility-of-rings-with-involution\/\" 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 purity with respect to modules of flat dimension at most one Mouhssine El-arabi and Youssef Najem Department of Mathematics, Moulay Ismail University, Morocco. Pages 291\u2013297 | Received 28 April 2023, Accepted 08 September 2023, Published 11 December 2023 Abstract The main goal of this <a class=\"read-more-link\" href=\"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/on-purity-with-respect-to-modules-of-flat-dimension-at-most-one\/\">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-2021","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2021","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=2021"}],"version-history":[{"count":5,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2021\/revisions"}],"predecessor-version":[{"id":2087,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2021\/revisions\/2087"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2021"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}