Some results on π-projective modules
Other Title(s)
بعض النتائج عن المقاسات من النمطπ
Dissertant
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
No. of Pages
99
Table of Contents
Table of contents.
Abstract.
Abstract in Arabic.
Introduction.
Chapter One : Basic concepts.
Chapter Two : π -projective modules and their properties.
Chapter Three : Some new characterizations of π-projective modules.
References.
American Psychological Association (APA)
Ulaywi, Ala Abbas. (2006). Some results on π-projective modules. (Doctoral dissertations Theses and Dissertations Master). University of Baghdad, Iraq
https://search.emarefa.net/detail/BIM-602938
Modern Language Association (MLA)
Ulaywi, Ala Abbas. Some results on π-projective modules. (Doctoral dissertations Theses and Dissertations Master). University of Baghdad. (2006).
https://search.emarefa.net/detail/BIM-602938
American Medical Association (AMA)
Ulaywi, Ala Abbas. (2006). Some results on π-projective modules. (Doctoral dissertations Theses and Dissertations Master). University of Baghdad, Iraq
https://search.emarefa.net/detail/BIM-602938
Language
English
Data Type
Arab Theses
Record ID
BIM-602938