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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 ganaiping78@163.com
XIANZHONG ZHAO*
Affiliation:
College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi, 330022, China email xianzhongzhao@263.net
*
✉xianzhongzhao@263.net
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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. 

References

Almeida, J., ‘Power varieties of semigroups I’, Semigroup Forum 33 (1986), 357–373.CrossRefGoogle Scholar
Almeida, J., ‘Power varieties of semigroups I I’, Semigroup Forum 33 (1986), 375–390.CrossRefGoogle Scholar
Almeida, J., ‘On power varieties of semigroups’, J. Algebra 120 (1989), 1–17.Google Scholar
Almeida, J., Finite Semigroups and Universal Algebra, Series in Algebra, 3 (World Scientific, Singapore, 1994), (translated from the 1992 Portuguese original and revised by the author).Google Scholar
Burris, S. and Sankappanavar, H. P., A Course in Universal Algebra (Springer, Berlin, 1981).Google Scholar
Crvenković, S., Dolinka, I. and Vinčić, M., ‘Involution semigroups are not globally determined’, Semigroup Forum 62 (2001), 477–481.Google Scholar
Fu, Y. Y. and Zhao, X. Z., ‘The closed subsemigroups of a Clifford semigroup’, Commun. Math. Res., to appear.Google Scholar
Gould, M. and Iskra, J. A., ‘Globally determined classes of semigroups’, Semigroup Forum 28 (1984), 1–11.Google Scholar
Gould, M. and Iskra, J. A., ‘Globals of completely regular periodic semigroups’, Semigroup Forum 29 (1984), 365–374.Google Scholar
Gould, M., Iskra, J. A. and Tsinakis, C., ‘Globally determined lattices and semilattices’, Algebra Universalis 19 (1984), 137–141.Google Scholar
Howie, J. M., Fundamentals of Semigroup Theory (Clarendon Press, Oxford, 1995).Google Scholar
Kobayashi, Y., ‘Semilattices are globally determined’, Semigroup Forum 29 (1984), 217–222.Google Scholar
McCarthy, D. J. and Hayes, D. L., ‘Subgroups of the power semigroup of a group’, J. Combin. Theory Ser A 14 (1973), 173–186.Google Scholar
Mogiljanskaja, E. M., ‘Non-isomorphic semigroups with isomorphic semigroups of subsets’, Semigroup Forum 6 (1973), 330–333.Google Scholar
Pin, J. E., ‘Power semigroups and related varieties of finite semigroups’, in: Semigroups and Their Applications (eds. Goberstein, S. M. and Higgins, P. M.) (Reidel Publishing Company, Dordrecht, 1987), 139–152.Google Scholar
Putcha, M. S., ‘Subgroups of the power semigroup of a finite semigroup’, Canad. J. Math. 21 (1979), 1077–1083.CrossRefGoogle Scholar
Sasaki, M., ‘Isomorphism problem of power semigroups of integer semigroup’, Annual Report Faculty of Education, Iwate University, Vol. 48(1) (1988), 123–126.Google Scholar
Tamura, T., ‘Unsolved problems on semigroups’, Sem. Reports of Math. Sci. (1967), 33–35.Google Scholar
Tamura, T., ‘Power semigroups of rectangular groups’, Math. Japon. 4 (1984), 671–678.Google Scholar
Tamura, T., ‘Isomorphism problem of power semigroups of completely 0-simple semigroups’, J. Algebra 98 (1986), 319–361.CrossRefGoogle Scholar
Tamura, T., ‘On the recent results in the study of power semigroups’, in: Semigroups and Their Applications (eds. Goberstein, S. M. and Higgins, P. M.) (Reidel Publishing Company, Dordrecht, 1987), 191–200.Google Scholar
Tamura, T. and Shafer, J., ‘Power semigroups’, Math. Japon. 12 (1967), 25–32.Google Scholar
Vinčić, M., ‘Global determinism of ∗-bands’, Filomat 33 (2001), 91–97.Google Scholar
Zhao, X. Z., ‘Idempotent semirings with a commutative additive reduct’, Semigroup Forum 64 (2002), 289–296.Google Scholar