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A Generalization of F-*regular* *Semigroups*

"... 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 ..."

Abstract
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S 0 such that (i) for each s ∈ S there is s 0 ∈ S 0 with ss 0 s = s, (ii) the idempotents of S 0 commute with the idempotents of S. In particular, we recapture a result due to McFadden, which states that each

*unit-regular**orthodox**semigroup*is an idempotent separating homomorphic image of a semidirect###
BEYOND *ORTHODOX* *SEMIGROUPS*

"... Abstract. We introduce the notions of a generalised category and of an inductive generalised category over a band. Our purpose is to describe a class of semigroups which we name weakly B-orthodox. In doing so we produce a new approach to characterising orthodox semigroups, by using inductive general ..."

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Abstract. We introduce the notions of a generalised category and of an inductive generalised category over a band. Our purpose is to describe a class of

*semigroups*which we name weakly B-*orthodox*. In doing so we produce a new approach to characterising*orthodox**semigroups*, by using inductive###
*Regular* *Semigroups* with a S0 − *Orthodox* Transversal

"... In this paper, we consider another generalization for quasi-ideal or-thodox transversal, the so-called S0-orthodox transversals. We give a structure theorem for regular semigroups with S0-orthodox transver-sals. If S0 is a S0-orthodox transversal of S then S can be described in terms of S0. ..."

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In this paper, we consider another generalization for quasi-ideal

*or-thodox*transversal, the so-called S0-*orthodox*transversals. We give a structure theorem for*regular**semigroups*with S0-*orthodox*transver-sals. If S0 is a S0-*orthodox*transversal of S then S can be described in terms of S0.###
A Multiplication Of E-Varieties Of *Orthodox* *Semigroups*

, 1995

"... We define semantically a partial multiplication on the lattice of all e-varieties of regular semigroups. In the case that the first factor is an e-variety of orthodox semigroups we describe our multiplication syntactically in terms of biinvariant congruences. ..."

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We define semantically a partial multiplication on the lattice of all e-varieties of

*regular**semigroups*. In the case that the first factor is an e-variety of*orthodox**semigroups*we describe our multiplication syntactically in terms of biinvariant congruences.###
E-UNITARY ALMOST FACTORIZABLE *ORTHODOX* *SEMIGROUPS*

"... Abstract. It is established that an E-unitary almost factorizable orthodox semigroup need not be isomorphic to a semidirect prod-uct of a band by a group, and a necessary and sufficient condition is given for an E-unitary almost factorizable orthodox semigroup to be isomorphic to such a semidirect p ..."

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Abstract. It is established that an E-unitary almost factorizable

*orthodox**semigroup*need not be isomorphic to a semidirect prod-uct of a band by a group, and a necessary and sufficient condition is given for an E-unitary almost factorizable*orthodox**semigroup*to be isomorphic to such a semidirect###
A REPRESENTATION OF THE FREE ELEMENTARY *ORTHODOX* *SEMIGROUP*

"... 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###
A MULTIPLICATION OF E {VARIETIES OF *ORTHODOX* *SEMIGROUPS*

"... This paper has been digitized, optimized for electronic delivery and stamped ..."

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This paper has been digitized, optimized for electronic delivery and stamped

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On Epiorthodox *Semigroups*

"... It has been well known that the band of idempotents of a naturally ordered orthodox semigroup satisfying the "strong Dubreil-Jacotin condition" forms a normal band. In the literature, the naturally ordered orthodox semigroups satisfying the strong Dubreil-Jacotin condition were first cons ..."

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It has been well known that the band of idempotents of a naturally ordered

*orthodox**semigroup*satisfying the "strong Dubreil-Jacotin condition" forms a normal band. In the literature, the naturally ordered*orthodox**semigroups*satisfying the strong Dubreil-Jacotin condition were first###
*Semigroups* Method for *semigroups* Version 2.0

"... The Semigroups package is a GAP package containing methods for semigroups, monoids, and inverse semi-groups, principally of transformations, partial permutations, bipartitions, subsemigroups of regular Rees 0-matrix semigroups, and the free inverse semigroup. Semigroups contains more efficient metho ..."

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The

*Semigroups*package is a GAP package containing methods for*semigroups*, monoids, and inverse*semi-groups*, principally of transformations, partial permutations, bipartitions, subsemigroups of*regular*Rees 0-matrix*semigroups*, and the free inverse*semigroup*.*Semigroups*contains more efficient