Share
المقاسات الجزيئة المقاسات المستحوذة على 2 وبعض اعماماتها == 2 - Absorbing Submdules (Modules) and Some of Their Generalizations
Author name:
عبد الرحمن عبد الله حرفش
Supervisor name:
انعام محمد علي هادي
General topic:
Mathematics
Specific topic:
Mathematics
Degree:
Master
University:
University of Baghdad
Language:
English
University location:
Baghdad
First pages:
27T1161 - p.pdf
Abstract:
Let R be a commutative ring with identity, and let M be a unitary left Rmodule. Prime ideals one of the main concepts in ring theory and many generalizations of this concept are introduced such as strongly prime ideals, almost prime ideals, weakly prime ideals, semi - prime ideals, weakly semiprime ideals and 2 - absorbing ideals. Moreover each of the above concepts generalized to submodules. Main goals in this work : Presenting a comprehensive study of 2 - absorbing submodules and giving many new characterizations and properties related with this concept. Also we use this concept to define and study a new class of modules which is called 2 - absorbing modules. Introducing and studying many generalizations of 2 - absorbing submodules, 2 - absorbing modules. In fact we introduce and study semi - 2 - absorbing submodules, semi - 2 - absorbing modules, Endo 2 - absorbing submodules, Endo semi - 2 - absorbing submodules, Endo 2 - absorbing modules and Endo semi - 2 - absorbing modules. Presenting other kinds of 2 - absorbing submodules(resp.2 - absorbing modules) namely small 2 - absorbing submodules (resp. small 2 - absorbing modules ). Then Endo small 2 - absorbing submodules (resp. Endo small 2absorbing modules) are introduced and studied.
