Discussion of a Doctorial Dissertation \u00a0in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:<\/p>\n
“Applications of Module Extension Banach Algebras “<\/strong><\/p>\n \u00a0<\/strong><\/p>\n In continuation of the scientific research movement and with the follow-up and presence of the Dean of the College of Computer Science and Mathematics<\/p>\n Prof. Dr. Duha Bashir Abdullah The Esteemed<\/strong><\/p>\n It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the \u00a0University of Mosul on Thursday \u00a09-11-2023<\/strong><\/p>\n Doctorial Dissertation by student Lamia Kader Ismail Khalil<\/strong><\/p>\n , under the supervision of Prof. Dr.<\/strong> Dr. Amir Abdulillah Mohammed Hussin<\/strong><\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><\/p>\n This thesis is based on similar to the study the properties of the linear mappings on Banach algebras by many researchers, we study and generalized some types of the derivations on module extension Banach algebra, depending on the two homomorphisms that effects on module extension Banach algebras.<\/p>\n Let \u00a0be module extension Banach –<\/strong>algebra and \u00a0be a Banach -bimodule, and let , \u00a0and \u00a0be continuous homomorphisms on \u00a0to . We proved the following:<\/p>\n If \u00a0is a module extension Banach algebra with zero product and every \u00a0and \u00a0are essential, then the continuous linear mapping \u00a0 is -anti derivation at zero, if and only if there exist a -anti derivation \u00a0and \u00a0such that \u00a0.<\/p>\n And we proved a continuous – local ternary derivation from unital module extension Banach -algebra into their periodical duals are symmetrical mapping and \u00a0-ternary derivation.<\/p>\n And also, if the continuous linear mapping on unital \u00a0is \u00a0-ternary derivation at the unite element (at zero), then:<\/p>\n In addition to that we proved, if \u00a0is a symmetric amenability such that \u00a0is weakly sequentially complete and \u00a0is essential, and the continuous linear mapping \u00a0from \u00a0into \u00a0is -Jorden derivation at zero, then there exists -derivation \u00a0and also there exists homomorphism , identifiers from \u00a0into \u00a0such that . We obtained similar results of the continuous linear mappings that are\u00a0 – – Jorden derivations at zero on module extension Banach -algebras.<\/p>\n Finally, we proved each – local higher derivation on a symmetric amenability module extension Banach algebra is – higher derivation. In addition to that, each – – anti local higher derivation on a symmetric amenability module extension Banach -algebra is – -higher derivation.<\/p>\n <\/p>\n The scientific committee included the following members:<\/p>\n prof.Dr. nizar hamdun shakr \u00a0– Chairman<\/p>\n prof. Dr. Ammar Siddiq Mahmoud – Member<\/p>\n prof. Dr. \u00a0Dr. Nada Yassin Qasim – Member<\/p>\n prof. Dr. husam qasim muhamad \u00a0– member<\/p>\n Ass. Prof. Dr. narin sabih muhamad \u00a0– Member<\/p>\n prof.Dr. Amir Abdulillah Mohammed Hussin – Member and supervisor<\/p>\n <\/p>\n \u00a0<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":" Discussion of a Doctorial Dissertation \u00a0in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled: “Applications of Module Extension Banach Algebras “ \u00a0 In continuation of the scientific research movement and with the follow-up and presence of the Dean of the College of Computer Science and Mathematics Prof. Dr. Duha Bashir Abdullah The Esteemed It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the \u00a0University of Mosul on Thursday \u00a09-11-2023 Doctorial Dissertation by student Lamia Kader Ismail Khalil , under the supervision of Prof. Dr. Dr. Amir Abdulillah Mohammed Hussin [Read More]<\/a><\/p>\n","protected":false},"author":24,"featured_media":37781,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-37780","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\/37780","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=37780"}],"version-history":[{"count":1,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/posts\/37780\/revisions"}],"predecessor-version":[{"id":37782,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/posts\/37780\/revisions\/37782"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/media\/37781"}],"wp:attachment":[{"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/media?parent=37780"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/categories?post=37780"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/tags?post=37780"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n