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Some Properties Associated with Adequate Transversals

Published online by Cambridge University Press:  20 November 2018

Xiangjun Kong
Xiangjun Kong*
Affiliation:
Department of Mathematics, Lanzhou University, Lanzhou, Gansu, 730000, P. R. China, and Department of Mathematics, Qufu Normal University, Qufu, Shandong, 273165, P. R. China e-mail: xiangjunkong97@163.com
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Abstract

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In this paper, another relationship between the quasi-ideal adequate transversals of an abundant semigroup is given. We introduce the concept of a weakly multiplicative adequate transversal and the classic result that an adequate transversal is multiplicative if and only if it is weakly multiplicative and a quasi-ideal is obtained. Also, we give two equivalent conditions for an adequate transversal to be weakly multiplicative. We then consider the case when $I$ and $\Lambda $ (defined below) are bands. This is analogous to the inverse transversal if the regularity condition is adjoined.

Keywords

20M10abundant semigroupadequate transversalGreen's ∗-relationsquasi-ideal

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 3 , 01 September 2011, pp. 487 - 497
Copyright
Copyright © Canadian Mathematical Society 2011

References

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