Abstract and Applied Analysis
Volume 2011 (2011), Article ID 353584, 6 pages
http://dx.doi.org/10.1155/2011/353584
Research Article

Tight Representations of 0- 𝐸 -Unitary Inverse Semigroups

Bahman Tabatabaie Shourijeh and Asghar Jokar

Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran

Received 3 June 2011; Revised 11 August 2011; Accepted 5 September 2011

Academic Editor: Detlev Buchholz

Copyright © 2011 Bahman Tabatabaie Shourijeh and Asghar Jokar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the tight representation of a semilattice in { 0 , 1 } by some examples. Then we introduce the concept of the complex tight representation of an inverse semigroup 𝑆 by the concept of the tight representation of the semilattice of idempotents 𝐸 of 𝑆 in { 0 , 1 } . Specifically we describe the tight representation of a 0- 𝐸 -unitary inverse semigroup and prove that if 𝜎 is a tight semilattice representation of the 0- 𝐸 -unitary inverse semigroup 𝑆 in { 0 , 1 } , then 𝜎 is a complex tight representation.