Some types of retractable and compressible modules

العناوين الأخرى

بعض أنواع من المقاسات المنضغطة و المنكمشة

مقدم أطروحة جامعية

Muslim, Isra Hasan

مشرف أطروحة جامعية

Mahmud, Layla Salman

الجامعة

جامعة بغداد

الكلية

كلية التربية للعلوم الصرفة-ابن الهيثم

القسم الأكاديمي

قسم الرياضيات

دولة الجامعة

العراق

الدرجة العلمية

ماجستير

تاريخ الدرجة العلمية

2016

الملخص الإنجليزي

Let R be a commutative ring with unity, M and N be (left) unitary R-modules.

Let Hom^(M,N) be the set of all R-homomorphisms from Mto N.

it is well-known that the properties of the R-module Hom^(M,N) are determined by the properties of R, M and N, and also some of the properties of M, N and R are determined by those of Hom^ (M, N) so for this reason , the study of Hom^(M,N) attracted the attention of many researchers.

Some special studies were appeared for Hom^(M,N) in case N is a non-zero submodule of M.

by using the restriction that Hom^ (M, N) ^0 whenever N is a non-zero submodule of M, such module M is called retractable module.

While when every non-zero submodule of M contains a copy of M, that means there exists a monomorphism in Hom^(M,N) whenever N is a non-zero submodule of M, M is called compressible module in this case.

Clearly the class of compressible modules is contained properly in the class of retractable modules .Many studies about these notions were given. Also some generalizations of these concepts were appeared such as essentially retractable modules, epi-retractable modules, small compressible and small retractable modules. In this work, we shall give detailed study about small compressible modules and small retractable modules.

Moreover we shall present other generalizations for compressible and retractable modules, namely, purely compressible modules, purely retractable modules, primely compressible modules and primely retractable modules.

التخصصات الرئيسية

الرياضيات

عدد الصفحات

120

قائمة المحتويات

• APA
• MLA
• AMA

لغة النص

الإنجليزية

نوع البيانات

رسائل جامعية

رقم السجل

BIM-737714