On φ-classes of modules

Dissertant

Abu Awdah, al-Husayn Kamal Muhammad

Thesis advisor

Ashur, Arwa Id
al-Ashqar, Muhammad Mahmud

Comitee Members

Mahdi, Hisham Bashir
Naji, Abd al-Karim Abd al-Qadir

University

Islamic University

Faculty

Faculty of Science

Department

Department of Mathematics

University Country

Palestine (Gaza Strip)

Degree

Master

Degree Date

2015

English Abstract

Let R be a commutative ring with identity and let M be a unitary R-module.

Let S(M) be the set of all submodules of M and :S(M)! S(M) S f;g be a function.

Let N be a proper submodule of M.

We say that N is -prime submodule of M if am 2 N - (N) where a 2 R, m 2 M implies that m 2 N or a 2 (N : M).

This concept was introduced by N.

Zamani ( see [39] ).

In this thesis we generalize the concept of -prime submodule to -primary submodule and also, we introduce the concept of -primal submodule, and we introduce the concept of -compactly packed module.

The concept of n-primly ideals in a commutative ring was introduced by A.E.Ashour [8].

In this thesis we generalize it to the concept of n-primly submodule.

Let N be a proper submodule of M, we say that N is 2-absorbing submodule if abm 2 N where a,b 2 R, m 2 M implies that ab 2 (N : M) or am 2 N or bm 2 N.

The concept of 2-absorbing submodule was introduced by A.

Darani and F.

Soheilnia ( see[19] ).

In this thesis, we generalize the concept of 2-absorbing submodule to -2-absorbing sub- module and we introduce the concept of 2-absorbing compactly packed module.

Main Subjects

Mathematics

No. of Pages

74

Table of Contents

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Language

English

Data Type

Arab Theses

Record ID

BIM-724333