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STRONGLY ORTHODOX CONGRUENCES ON AN
$E$-INVERSIVE SEMIGROUP
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 96 / Issue 2 / April 2014
- Published online by Cambridge University Press:
- 01 April 2014, pp. 216-230
- Print publication:
- April 2014
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- Article
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In this paper we investigate some subclasses of strongly regular congruences on an
$E$-inversive semigroup 
$S$. We describe the minimum and the maximum strongly orthodox congruences on 
$S$ whose characteristic trace coincides with the characteristic trace of given congruences and, in each case, we present an alternative characterization for them. A description of all strongly orthodox congruences on 
$S$ with characteristic trace 
$\tau $ is given. Further, we investigate the kernel relation of strongly orthodox congruences on an 
$E$-inversive semigroup and give the least and the greatest element in the class of the same kernel with a given congruence.
