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"... � in terms of idempotentgenerated regular semigroup E, with a medial idempotent u, and of the orthodox semigroups with identity S, such that ES ( ) � u E u. In that paper M. Loganathan has also shown, that every regular semigroup S with a medial idempotent u, can be described in terms of the subse ..."
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of the subsemigroup of S generated by the set of idempotents E � E ( S) and the orthodox subsemigroup of S with identity, uSu. In this paper we will prove that W � W ( E, S) constructed by Loganathan is regular semigroup with a medial idempotent.
FUNDAMENTAL SEMIGROUPS HAVING A BAND OF IDEMPOTENTS
, 2007
"... The construction by Hall of a fundamental orthodox semigroup WB from a band B provides an important tool in the study of orthodox semigroups. We present here a semigroup SB that plays the role of WB for a class of semigroups having a band of idempotents B. Specifically, the semigroups we consider a ..."
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are weakly Babundant and satisfy the congruence condition (C). Any orthodox semigroup S with E(S) = B lies in our class. On the other hand, if a semigroup S lies in our class, then S is Ehresmann if and only if B is a semilattice. The Hall semigroup WB is a subsemigroup of SB, as are the (weakly
Strongly Regular Congruences on
"... Copyright c © 2014 Hengwu Zheng and Yunlong Yu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. It is shown that every strongly regul ..."
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regular congruence on an Einversive semigroup is uniquely determined by its kernel and hypertrace. Furthermore, strongly orthodox (resp., strongly regular) congruences on an Einversive (resp., Einversive E)semigroup S are described in terms of certain congruence pairs (ξ,K), where ξ is a certain
A Generalization of Fregular Semigroups
"... A regular semigroup S is termed locally Fregular, if each class of the least completely simple congruence ξ contains a greatest element with respect to the natural partial order. It is shown that each locally Fregular semigroup S admits an embedding into a semidirect product of a band by S/ξ. Furt ..."
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/ξ. The main result contains our recent representation theorem for Fregular semigroups [1], whence McAlister’s characterization of Finverse semigroups [2]. Finally, we establish that an orthodox semigroup S is a homomorphic image of an Fregular semigroup, if and only if it contains an inverse subsemigroup
Comprehensive Congruences on UCyber Semigroups
"... An Ucyber semigroup S is an idempotentconnected Uabundant semigroup whose subset U forms a subsemigroup of S. In this paper, we consider an admissible relation “σ ” defined on such a semigroup. In fact, an Ucyber semigroup is a special Usemiabundant semigroup which is a generalization of an ort ..."
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An Ucyber semigroup S is an idempotentconnected Uabundant semigroup whose subset U forms a subsemigroup of S. In this paper, we consider an admissible relation “σ ” defined on such a semigroup. In fact, an Ucyber semigroup is a special Usemiabundant semigroup which is a generalization
Covers for Monoids
"... In this contribution to the structure theory of semigroups, we propose a unified generalisation of a string of results on group extensions, originating on the one hand in the seminal structure and covering theorems of McAlister and on the other, in Ash's celebrated solution of the Rhodes conje ..."
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conjecture in finite semigroup theory. McAlister proved that each inverse monoid admits an Eunitary cover, and gave a structure theorem for Eunitary inverse monoids. Subsequent generalisations extended one or both results to orthodox monoids (McAlister, Szendrei, Takizawa), regular monoids (Trotter), E
A REPRESENTATION OF THE FREE ELEMENTARY ORTHODOX SEMIGROUP
"... Abstract. The free elementary inverse semigroup 27 has a simple representation as a semigroup of transformations on the set of integers. In this note, we obtain a fairly simple representation of a preimage of 27, the free elementary orthodox semigroup (9. Let (9(I) denote the free elementary ortho ..."
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Abstract. The free elementary inverse semigroup 27 has a simple representation as a semigroup of transformations on the set of integers. In this note, we obtain a fairly simple representation of a preimage of 27, the free elementary orthodox semigroup (9. Let (9(I) denote the free elementary