Some types of retractable and compressible modules

Other Title(s)

بعض أنواع من المقاسات المنضغطة و المنكمشة

Dissertant

Muslim, Isra Hasan

Thesis advisor

Mahmud, Layla Salman

University

University of Baghdad

Faculty

College of Education for Puresciences-IBN al-Haitham

Department

Department of Mathematics

University Country

Iraq

Degree

Master

Degree Date

2016

English Abstract

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.

Main Subjects

Mathematics

No. of Pages

120

Table of Contents

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Language

English

Data Type

Arab Theses

Record ID

BIM-737714