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A Multiplication of E-Varieties of Regular Solid *Semigroups* by Inverse *Semigroup* Varieties

, 1997

"... . A multiplication of e-varieties of regular E-solid semigroups by inverse semigroup varieties is described both semantically and syntactically. The associativity of the multiplication is also proved. 1. Introduction We investigate here an operator on the lattice of all e-varieties of regular semig ..."

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is an e-variety of

*orthodox**semigroups*we also described our multiplication syntactically in terms of biinvariant congruences for*orthodox**semigroups*introduced in [5] by Ka#ourek and Szendrei. In this paper we present a syntactical description of our multiplication in the case that the first factor###
PARTIAL ORDERS IN REGULAR *SEMIGROUPS*

, 2010

"... First we have obtained equivalent conditions for a regular semi-group and is equivalent to N = N1 It is observed that every regular semigroup is weakly separative and C ⊆ S and on a completely reg-ular semigroup S ⊆ N and S is partial order. It is also obtained that a band (S,.) is normal iff C = N. ..."

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Classes of *semigroups* modulo Green’s relation H

"... Inverses semigroups and orthodox semigroups are either defined in terms of inverses, or in terms of the set of idempotents E(S). In this article, we study analogs of these semigroups defined in terms of inverses modulo Green’s relation H, or in terms of the set of group invertible elements H(S), tha ..."

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Inverses

*semigroups*and*orthodox**semigroups*are either defined in terms of inverses, or in terms of the set of idempotents E(S). In this article, we study analogs of these*semigroups*defined in terms of inverses modulo Green’s relation H, or in terms of the set of group invertible elements H###
Comprehensive Congruences on U-Cyber *Semigroups*

"... 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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of an

*orthodox**semigroup*and also a type W*semigroup*. We will prove that the admissible relation “σ ” defined on an U-cyber*semigroup*is a comprehensive congruence and consequently,a related result previously obtained by X. J. Guo on IC quasi-adequate*semigroups*in 2001 is extended to U-cyber*semigroups*###
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 ..."

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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### Index Term—

"... � 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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� 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###
Orthocryptic rpp *Semigroups*

, 2009

"... A strongly rpp semigroup S is called orthocryptic rpp semigroup if (1) the set of idempotents forms a band; and (2) the relation H(†) is a congruence. Some characterizations of orthodox cryptic rpp semigroups are obtained. In particular, it is proved that a semigroup is a orthocryptic rpp semigroup ..."

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A strongly rpp

*semigroup*S is called orthocryptic rpp*semigroup*if (1) the set of idempotents forms a band; and (2) the relation H(†) is a congruence. Some characterizations of*orthodox*cryptic rpp*semigroups*are obtained. In particular, it is proved that a*semigroup*is a orthocryptic rpp*semigroup*### BANDS WITH HIGH SYMMETRY AND UNIFORM BANDS

, 2012

"... In this dissertation we will be focused on determining classes of bands which are embeddable into some band with high symmetry. It is known that rectangular bands have high symmetry and every semilattice is embeddable into a semilattice with high symmetry. We will try to expand on these classes as m ..."

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*semigroups*for which the band of idempotents is embeddable into a band with high symmetry. We finish the dissertation by showing the result that every band is embeddable into a uniform band. From this, it will then follow that every

*orthodox*

*semigroup*is embeddable into a bisimple

*orthodox*

*semigroup*.

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Left Semiregular−U−liberal *Semigroups*

"... In this paper, we introduce the left semiregular−U−liberal semi-groups which are orthodox U−liberal semigroups whose set of projec-tions are left semiregular bands. Some structure theorems are obtained. At last, we describe the isomorphisms between two left semiregular −U−liberal semigroups. ..."

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In this paper, we introduce the left semiregular−U−liberal

*semi-groups*which are*orthodox*U−liberal*semigroups*whose set of projec-tions are left semiregular bands. Some structure theorems are obtained. At last, we describe the isomorphisms between two left semiregular −U−liberal*semigroups*.###
Semi-abundant *Semigroups* with Quasi-Ehresmann Transversals

"... Abstract. Chen (Communications in Algebra 27(2), 4275-4288, 1999) introduced and investigated ortho-dox transversals of regular semigroups. In this paper, we initiate the investigation of quasi-Ehresmann transversals of semi-abundant semigroups which are generalizations of orthodox transversals of r ..."

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Abstract. Chen (Communications in Algebra 27(2), 4275-4288, 1999) introduced and investigated

*ortho-dox*transversals of regular*semigroups*. In this paper, we initiate the investigation of quasi-Ehresmann transversals of semi-abundant*semigroups*which are generalizations of*orthodox*transversals