Paper Information

Title: 

ON THE COMMUTATIVITY DEGREE IN ALGEBRAIC STRUCTURES

Type: PAPER
Author(s): AHMADI DALIR K.*,DOUSTI H.,CAMPBELL C.M.
 
 *MATHEMATICS DEPARTMENT, FACULTY OF BASIC SCIENCES, ISLAMIC AZAD UNIVERSITY, TABRIZ BRANCH TABRIZ, IRAN
 
Name of Seminar: SEMINAR ON ALGEBRA (SALG20)
Type of Seminar:  CONFERENCE
Sponsor:  TARBIAT MOALLEM UNIVERSITY, FACULTY OF MATHEMATICAL SCIENCES AND COMPUTER
Date:  2009Volume 20
 
 
Abstract: 

The commutativity degree of groups and rings has been studied by certain authors since 1973, and the main result obtained is Pr(A)£ 5/8 , where Pr(A) is the commutativity degree of a non-abelian group (or ring) A. Verifying this inequality for an arbitrary semigroup A is a natural question and in this paper by presenting an infinite class of finite noncommutative semigroups we prove that the commutativity degree may be arbitrarily close to 1. We name this class of semigroups the almost commutative or approximately abelian semigroups.

 
Keyword(s): COMMUTATIVITY DEGREE, PRESENTATION OF ALGEBRAIC STRUCTURES GROUPS, SEMIGROUPS AND MONOIDS
 
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