Almost Commutative Semigroups-Reference-Cited by-同舟云学术

Almost Commutative Semigroups

Published:2011-12 Issue:spec01 Volume:18 Page:881-888
ISSN:1005-3867
Container-title:Algebra Colloquium
language:en
Short-container-title:Algebra Colloq.

Author:

Ahmadidelir K.¹,Campbell C. M.²,Doostie H.³

Affiliation:

1. Department of Mathematics, Faculty of Basic Sciences, Tabriz Branch, Islamic Azad University, P.O. Box 1655, Tabriz, Iran

2. School of Mathematics and Statistics, University of St. Andrews, North Haugh, St. Andrews, Fife KY16 9SS, Scotland

3. Mathematics Department, Science and Research Branch, Islamic Azad University, Tehran, P.O. Box 14515/1775, Iran

Abstract

The commutativity degree of groups and rings has been studied by certain authors since 1973, and the main result obtained is [Formula: see text], 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 non-commutative 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1005386711000769

Reference20 articles.

1. Comparing Semigroup and Monoid Presentations for Finite Monoids

2. On defining groups efficiently without using inverses

3. Fibonacci semigroups

4. Semigroup and Group Presentations

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