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by O. Hysa, Semigroup W W E, I. Some Preliminares
"... � in terms of idempotent-generated 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.

A REPRESENTATION OF THE FREE ELEMENTARY ORTHODOX SEMIGROUP

by Carl Eberhart, Wiley Williams
"... Abstract. The free elementary inverse semigroup 27 has a simple representa-tion as a semigroup of transformations on the set of integers. In this note, we obtain a fairly simple representation of a pre-image 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 representa-tion as a semigroup of transformations on the set of integers. In this note, we obtain a fairly simple representation of a pre-image of 27, the free elementary orthodox semigroup (9. Let (9(I) denote the free elementary

FUNDAMENTAL SEMIGROUPS HAVING A BAND OF IDEMPOTENTS

by Gracinda M. S. Gomes, Victoria Gould , 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 B-abundant 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

by E-inversive Semigroups, Hengwu Zheng, Yunlong Yu
"... 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 E-inversive semigroup is uniquely determined by its kernel and hyper-trace. Fur-thermore, strongly orthodox (resp., strongly regular) congruences on an E-inversive (resp., E-inversive E-)semigroup S are described in terms of certain congruence pairs (ξ,K), where ξ is a certain

A Generalization of F-regular Semigroups

by Bernd Billhardt
"... A regular semigroup S is termed locally F-regular, 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 F-regular 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 F-regular semigroups [1], whence McAlister’s characterization of F-inverse semigroups [2]. Finally, we establish that an orthodox semigroup S is a homomorphic image of an F-regular semigroup, if and only if it contains an inverse subsemigroup

Comprehensive Congruences on U-Cyber Semigroups

by Yin Qingyan, Ren Xueming, K. P. Shum
"... An U-cyber semigroup S is an idempotent-connected U-abundant 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 U-cyber semigroup is a special U-semiabundant semigroup which is a generalization of an ort ..."
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An U-cyber semigroup S is an idempotent-connected U-abundant 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 U-cyber semigroup is a special U-semiabundant semigroup which is a generalization

Covers for Monoids

by John Fountain, Jean-Eric Pin, Pascal Weil
"... 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 E-unitary cover, and gave a structure theorem for E-unitary inverse monoids. Subsequent generalisations extended one or both results to orthodox monoids (McAlister, Szendrei, Takizawa), regular monoids (Trotter), E
Results 1 - 7 of 7