Compactly packed modules over noncommutative rings
Dissertant
Thesis advisor
Ashur, Arwa Id
al-Ashker, Muhammad Mahmud
University
Islamic University
Faculty
Faculty of Science
Department
Department of Mathematics
University Country
Palestine (Gaza Strip)
Degree
Master
Degree Date
2016
English Abstract
Let R be an associative ring with identity and M be a unitary right R-module.
A proper submodule N of M is compactly packed if for each family fP g 2 of prime submodules of M with N S 2 P , N P for some 2 .
A module M is called compactly packed if every proper submodule of M is compactly packed.
This concept of compactly packed modules was introduced over several submodules such as primary and primal submodules, instead of prime submodules over commutative rings.
Also this concept was generalized over noncommutative rings with identity for prime and primary submodules.
In this thesis, we generalize these concepts for weakly compactly packed and weakly primary compactly packed modules and introduce the concepts of primal compactly packed modules over noncommutative rings.
We also introduce the concept of weakly primal compactly packed modules.
A submodules N of M is called a weakly primal submodule if the set P = wadj(N)[f0g forms an ideal of R where wadj(N) is the set of elements of R that are not right weakly prime to N, (remember that an element r 2 R is not right weakly prime to N if 0 6= eRr N for some e 2 M n N).
Main Subjects
No. of Pages
88
Table of Contents
Table of contents.
Abstract.
Introduction.
Chapter One : Preliminaries
Chapter Two : Weakly compactly packed rings.
Chapter Three : Compactly packed modules.
Chapter Four : Classes of weakly compactly packed modules.
Conclusions.
References.
American Psychological Association (APA)
Abu Suawin, Sulayman. (2016). Compactly packed modules over noncommutative rings. (Master's theses Theses and Dissertations Master). Islamic University, Palestine (Gaza Strip)
https://search.emarefa.net/detail/BIM-688606
Modern Language Association (MLA)
Abu Suawin, Sulayman. Compactly packed modules over noncommutative rings. (Master's theses Theses and Dissertations Master). Islamic University. (2016).
https://search.emarefa.net/detail/BIM-688606
American Medical Association (AMA)
Abu Suawin, Sulayman. (2016). Compactly packed modules over noncommutative rings. (Master's theses Theses and Dissertations Master). Islamic University, Palestine (Gaza Strip)
https://search.emarefa.net/detail/BIM-688606
Language
English
Data Type
Arab Theses
Record ID
BIM-688606