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Journal ArticleDOI

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.

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Citations
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Journal ArticleDOI
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

Journal ArticleDOI
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
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Book
01 Jan 1976

1,294 citations

Journal ArticleDOI

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]....

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Journal Article

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....

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Journal ArticleDOI
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....

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

    [...]