# Lattice of idempotent separating congruences in a ℙ-regular semigroup

01 Jun 1992-Bulletin of The Australian Mathematical Society (Cambridge University Press (CUP))-Vol. 45, Iss: 3, pp 483-488

TL;DR: In this paper, the concept of ℙ-regular, normal subset of a regular semigroup is introduced, and the maximum idempotent separating congruence in a regular semi-commodity is described.

Abstract: In this paper we introduce the concept of ℙ-regular, normal subset of a ℙ-regular semigroup, give an alternate characterisation of the maximum idempotent separating congruence in a ℙ-regular semigroup and finally describe the lattice of the idempotent separating congruences in a ℙ-regular semigroup.

##### Citations

More filters

••

TL;DR: In this article, the authors describe the strong\(\mathcal{P})-congruences on regular regular semigroups in terms of their characteristic kernels and characteristic traces.

Abstract: In this paper we describe the strong\(\mathcal{P}\)-congruences on\(\mathcal{P}\)-regular semigroups in terms of their characteristic kernels and characteristic traces.

4 citations

••

TL;DR: In this paper, the minimum and the maximum strongly orthodox congruences on a strongly regular semigroup with characteristic trace $S$ fixme $σσϵσεσετε τϵε τσσεε τεσõεστε εσασατεσα τσεβσα βασβασε βαβατα ββαβδαββα βγαβγβαγαγ βαγγγααγβγ

Abstract: 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.

2 citations

##### References

More filters

••

304 citations

01 Jan 1993

220 citations

### "Lattice of idempotent separating co..." refers background in this paper

...Unless otherwise defined, our notation will be that of [2]....

[...]

•

15 citations

### "Lattice of idempotent separating co..." refers background in this paper

...EsThen (5, P) is called a P-regular semigroup [5] if it satisfies the following: (1) P(2) C Es (2) for each q&P, qPqC P....

[...]

...7 of [5] there exists a unique 6+ G Vp(6) such that 66+ = aa and bb — a+a....

[...]

••

TL;DR: In this article, a more precise description of ρ and σ is given, where the largest congruence ρ is defined as a partition of the set E of idempotents of S satisfying certain normality conditions.

Abstract: Any congruence on an orthodox semigroup S induces a partition of the set E of idempotents of S satisfying certain normality conditions. Meakin (1970) has characterized those partitions of E which are induced by congruences on S as well as the largest congruence ρ and the smallest congruence σ on S corresponding to such a partition of E . In this paper a more precise description of ρ and σ is given.

13 citations

### "Lattice of idempotent separating co..." refers background or methods in this paper

...In this paper firstly we give an alternate characterisation of T and secondly we give a description of the lattice of idempotent separating congruences on a P-regular semigroup 5 , which generalises Feigenbaum's result [1] for orthodox semigroups....

[...]

...3 of [1] due to Feigenbaum, because in that case a, b £ K implies a, b £ C(E)....

[...]