Compactly packed modules over noncommutative rings

Dissertant

Abu Suawin, Sulayman

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

Mathematics

No. of Pages

88

Table of Contents

• APA
• MLA
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Language

English

Data Type

Arab Theses

Record ID

BIM-688606