Strongly derivation pairs on prime and semi prime rings

Other Title(s)

الاشتقاقات المزدوجة القوية في الحلقات الأولية وشبه الأولية

Dissertant

Yass, Shayma Badr

Thesis advisor

Majid, Abd al-Rahman Hamid

University

University of Baghdad

Faculty

College of Science

Department

Mathematics Department

University Country

Iraq

Degree

Master

Degree Date

2010

English Abstract

Let R be an associative ring.

The main purpose of this work: Firstly; studying the commutativity of prime rings under certain conditions, it comes through (i) Studying generalized derivations and giving a result similar to Ashraf et al., but in different conditions, (ii) Extending the notation of the generalized derivation, to, two generalized derivations associated with the same derivation, as a new idea.

Secondly; studying the commutativity of semiprime rings under certain conditions, it comes through (i) Introducing the definition of generalized left derivation (generalized Jordan left derivation) associated with left derivation, as a special case, of the definition that introduced by Ashraf and Ali, (ii) Introducing and studying the concept of generalized reverse derivation, through this study, we generalize Samman's and Al- Yamani's theorem and, Daif's and Bell's theorem, for a generalized reverse derivation.

Thirdly; presenting the definition of strongly derivation pair and Jordan strongly derivation pair on a ring R, and studying the relation between them.

Also, we study prime rings, semiprime rings, and rings that have commutator left nonzero divisors with strongly derivation pairs, to obtain the notation of derivations.

Main Subjects

Mathematics

Topics

• Mathematics
• Mathematical analysis
• Algebra
• Algebraic fields

No. of Pages

96

Table of Contents

• APA
• MLA
• AMA

Language

English

Data Type

Arab Theses

Record ID

BIM-602250