Abstract view
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Some Properties Associated with Adequate Transversals
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Published:2011-02-16
Printed: Sep 2011
Xiangjun Kong,
Department of Mathematics, Lanzhou University, Lanzhou, Gansu, 730000, P. R. China
Abstract
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.
