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REGULAR SEMIGROUPS WITH NORMAL IDEMPOTENTS

Part of: Semigroups

Published online by Cambridge University Press:  29 March 2017

XIANGFEI NI  and
HAIZHOU CHAO
XIANGFEI NI*
Affiliation:
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, PR China email nxf@zjnu.cn
HAIZHOU CHAO
Affiliation:
Department of Mathematics, Shanghai University of Finance and Economics, Zhejiang College, Jinhua 321004, PR China email yfzcxjt@163.com
*
✉nxf@zjnu.cn
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Abstract

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In this paper, we investigate regular semigroups that possess a normal idempotent. First, we construct a nonorthodox nonidempotent-generated regular semigroup which has a normal idempotent. Furthermore, normal idempotents are described in several different ways and their properties are discussed. These results enable us to provide conditions under which a regular semigroup having a normal idempotent must be orthodox. Finally, we obtain a simple method for constructing all regular semigroups that contain a normal idempotent.

Keywords

regular semigroupnormal idempotentorthodox semigroup

MSC classification

Primary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 103 , Issue 1 , August 2017 , pp. 116 - 125
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

Footnotes

This project is supported by the National Natural Science Foundation of China (grant no. 11401534).

References

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Blyth, T. S. and McFadden, R. B., ‘On the construction of a class of regular semigroups’, J. Algebra 81 (1983), 1–22.Google Scholar
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