Some results on π-projective modules

Other Title(s)

بعض النتائج عن المقاسات من النمطπ

Dissertant

Ulaywi, Ala Abbas

Thesis advisor

al-Hashimi, Basil Ata
Naum, Adil Ghassan

University

University of Baghdad

Faculty

College of Science

Department

Mathematics Department

University Country

Iraq

Degree

Ph.D.

Degree Date

2006

English Abstract

Let R be an associative ring with identity .A unital left module M over R is said to be π-projective module if for any two submodules A, B of M with A+B=M, there exists fÎEnd(M) with Im(f)ÍA and Im(If)ÍB.

The aim of this thesis is to give a comprehensive study of π- projective modules and to obtain some new properties of this class of modules.

In this work, we also try to characterize left perfect rings, semiperfect rings and semisimple rings using π-projective modules.

One of our main results is to dualize the notation of IkedaNakayama module (IN-module) and use it to derive various characterizations for modules with this property, We call an R-module M an Co-Ikeda-Nakayama module ((IN)* -module) if T (A B) T (A) T (B) s s s + = + for any submodules A and B of M with S=End(M) and T (A) ={f s ÎS:f(M)ÍA}.

In particular, we show that π- projective modules are those modules for which S=T (A) T (B) s s + whenever A+B=M.

Main Subjects

Mathematics

No. of Pages

99

Table of Contents

• APA
• MLA
• AMA

Language

English

Data Type

Arab Theses

Record ID

BIM-602938