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GLOBAL DETERMINISM OF CLIFFORD SEMIGROUPS

Part of: Ordered sets Semigroups

Published online by Cambridge University Press:  16 May 2014

AIPING GAN  and
XIANZHONG ZHAO
AIPING GAN
Affiliation:
Department of Mathematics, Northwest University, Xi’an, Shaanxi, 710127, China College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi, 330022, China email [email protected]
XIANZHONG ZHAO*
Affiliation:
College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi, 330022, China email [email protected]
*
✉[email protected]
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Abstract

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In this paper we shall give characterizations of the closed subsemigroups of a Clifford semigroup. Also, we shall show that the class of all Clifford semigroups satisfies the strong isomorphism property and so is globally determined. Thus the results obtained by Kobayashi [‘Semilattices are globally determined’, Semigroup Forum29 (1984), 217–222] and by Gould and Iskra [‘Globally determined classes of semigroups’ Semigroup Forum28 (1984), 1–11] are generalized.

Keywords

Clifford semigroupclosed subsemigrouppower semigroup

MSC classification

Secondary: 06A12: Semilattices 20M17: Regular semigroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 97 , Issue 1 , August 2014 , pp. 63 - 77
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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