{"id":41256,"date":"2025-08-25T19:43:28","date_gmt":"2025-08-25T19:43:28","guid":{"rendered":"https:\/\/uomosul.edu.iq\/en\/computerscience\/?p=41256"},"modified":"2025-08-25T19:43:40","modified_gmt":"2025-08-25T19:43:40","slug":"1-253","status":"publish","type":"post","link":"https:\/\/uomosul.edu.iq\/en\/computerscience\/2025\/08\/25\/1-253\/","title":{"rendered":"Master\u2019s thesis by Student \u00a0Mohammed Ismael Jumaah Salman"},"content":{"rendered":"<p>Discussion of the master\u2019s thesis in the College of Computer Science and Mathematics -Department of<\/p>\n<p>Mathematics Sciences entitled:<\/p>\n<p><strong>&#8220;<\/strong> <strong>The Four Potent Nil Clean Rings<\/strong><strong>&#8220;<\/strong><\/p>\n<p>It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on <strong>Monday<\/strong>,25 \u00a0-8-2025.<\/p>\n<p>Master\u2019s thesis by <strong>Student \u00a0<\/strong><strong>Mohammed Ismael Jumaah Salman <\/strong><\/p>\n<p><strong>under<\/strong> <strong>the supervision of<\/strong><strong> Prof. Dr. Nazar Hamdoon Shuker<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>A ring\u00a0 is said to be four potent if every element\u00a0 satisfies the identity. \u00a0for every . This thesis begins by establishing the fundamental properties of four potent rings. It then introduces the concept of a generalized four potent ring, in which each element\u00a0 satisfies , meaning that the square of each element is four potent. The core structural properties of such rings are studied in detail. The relationships between generalized four potent rings and other algebraic structures, such as strongly 2-nil clean rings, are examined. Furthermore, the thesis introduces and investigates generalized four potent nil clean rings, focusing on their defining characteristics. Special emphasis is placed on the role of the Jacobson radical and the right singular ideal within these rings. All results are supported by rigorous proofs, and illustrative examples are provided to clarify the theoretical findings.<\/p>\n<p><strong>The scientific committee included the following members:<\/strong><\/p>\n<ul>\n<li><strong> Dr. Husam Qasem Mohammad<\/strong> \u2013 <strong>Chairman<\/strong><\/li>\n<li><strong> Prof. Dr. Bedaa Suhel Abdulla &#8211; Member.<\/strong><\/li>\n<li><strong> Prof. Dr. Zubaida Muhammed Ibrahem &#8211; Member.<\/strong><\/li>\n<li><strong> Dr. Nazar Hamdoon Shuker &#8211; Member and supervisor.<\/strong><\/li>\n<\/ul>\n<p><strong>\u00a0<\/strong><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Discussion of the master\u2019s thesis in the College of Computer Science and Mathematics -Department of Mathematics Sciences entitled: &#8220; The Four Potent Nil Clean Rings&#8220; It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Monday,25 \u00a0-8-2025. Master\u2019s thesis by Student \u00a0Mohammed Ismael Jumaah Salman under the supervision of Prof. Dr. Nazar Hamdoon Shuker &nbsp; A ring\u00a0 is said to be four potent if every element\u00a0 satisfies the identity. \u00a0for every . This thesis begins by establishing the fundamental properties of four potent rings. It then introduces the concept of <a href=\"https:\/\/uomosul.edu.iq\/en\/computerscience\/2025\/08\/25\/1-253\/\"> [Read More]<\/a><\/p>\n","protected":false},"author":24,"featured_media":41257,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-41256","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-viva"],"_links":{"self":[{"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/posts\/41256","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/users\/24"}],"replies":[{"embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/comments?post=41256"}],"version-history":[{"count":1,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/posts\/41256\/revisions"}],"predecessor-version":[{"id":41258,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/posts\/41256\/revisions\/41258"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/media\/41257"}],"wp:attachment":[{"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/media?parent=41256"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/categories?post=41256"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/tags?post=41256"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}