scholarly journals On Vn-semigroups

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Ze Gu ◽  
Xilin Tang
Keyword(s):  
Regular Semigroups ◽  
New Class ◽  
Orthodox Semigroups

AbstractIn this paper, we give some new characterizations of orthodox semigroups in terms of the set of inverses of idempotents. As a generalization, a new class of regular semigroups, namely V

scholarly journals A NEW CONSTRUCTION FOR REGULAR SEMIGROUPS WITH QUASI-IDEAL ORTHODOX TRANSVERSALS

2009 ◽  
Vol 86 (2) ◽  
pp. 177-187 ◽  
Author(s):  
XIANGJUN KONG ◽  
XIANZHONG ZHAO
Keyword(s):  
Regular Semigroup ◽  
Structure Theorem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Green’S Relations ◽  
Regular Semigroups ◽  
New Construction ◽  
Necessary And Sufficient ◽  
Equivalent Conditions ◽  
Orthodox Semigroups

AbstractIn any regular semigroup with an orthodox transversal, we define two sets R and L using Green’s relations and give necessary and sufficient conditions for them to be subsemigroups. By using R and L, some equivalent conditions for an orthodox transversal to be a quasi-ideal are obtained. Finally, we give a structure theorem for regular semigroups with quasi-ideal orthodox transversals by two orthodox semigroups R and L.

scholarly journals Identities for existence varieties of regular semigroups

1989 ◽  
Vol 40 (1) ◽  
pp. 59-77 ◽  
Author(s):  
T.E. Hall
Keyword(s):  
Type Theorem ◽  
Inverse Semigroups ◽  
Direct Products ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Existence Variety ◽  
Completely Regular Semigroups ◽  
Locally Inverse Semigroups ◽  
Orthodox Semigroups ◽  
Regular Rings

A natural concept of variety for regular semigroups is introduced: an existence variety (or e-variety) of regular semigroups is a class of regular semigroups closed under the operations H, Se, P of taking all homomorphic images, regular subsernigroups and direct products respectively. Examples include the class of orthodox semigroups, the class of (regular) locally inverse semigroups and the class of regular E-solid semigroups. The lattice of e-varieties of regular semigroups includes the lattices of varieties of inverse semigroups and of completely regular semigroups. A Birkhoff-type theorem is proved, showing that each e-variety is determined by a set of identities: such identities are then given for many e-varieties. The concept is meaningful in universal algebra, and as for regular semigroups could give interesting results for e-varieties of regular rings.

Structure of Strict Abundant Semigroups

2019 ◽  
Vol 26 (03) ◽  
pp. 387-400
Author(s):  
Yizhi Chen ◽  
Bo Yang ◽  
Aiping Gan
Keyword(s):  
Tree Structure ◽  
General Construction ◽  
Regular Semigroups ◽  
New Class ◽  
Abundant Semigroups ◽  
Structure Theorems ◽  
Subdirect Products

We introduce a new class of semigroups called strict abundant semigroups, which are concordant semigroups and subdirect products of completely [Formula: see text]-simple abundant semigroups and completely 0-[Formula: see text]-simple primitive abundant semigroups. A general construction and a tree structure of such semigroups are established. Consequently, the corresponding structure theorems for strict regular semigroups given by Auinger in 1992 and by Grillet in 1995 are generalized and extended. Finally, an example of strict abundant semigroups is also given.

E-SOLID E-VARIETIES OF REGULAR SEMIGROUPS WHICH ARE BIEQUATIONAL

1996 ◽  
Vol 06 (03) ◽  
pp. 277-290 ◽  
Author(s):  
RAYMOND BROEKSTEEG
Keyword(s):  
Regular Semigroups ◽  
Orthodox Semigroups

We extend the notion of biidentity from bivarieties of orthodox semigroups to e-varieties of regular semigroups. We show that an E-solid e-variety ε may be described in terms of biidentities (within the e-variety of all regular semigroups) if and only if there is an integer n≥2 such that for each pair e, f of idempotents of each member of ε, we have that (ef)n=ef.

Boolean Congruence Lattices of Orthodox Semigroups

1991 ◽  
Vol 43 (2) ◽  
pp. 225-241 ◽  
Author(s):  
Karl Auinger
Keyword(s):  
Inverse Semigroups ◽  
Regular Semigroups ◽  
Commutative Semigroups ◽  
Completely Regular ◽  
Clifford Semigroups ◽  
Congruence Lattices ◽  
Completely Regular Semigroups ◽  
Orthodox Semigroups

The problem of characterizing the semigroups with Boolean congruence lattices has been solved for several classes of semigroups. Hamilton [9] and the author of this paper [1] studied the question for semilattices. Hamilton and Nordahl [10] considered commutative semigroups, Fountain and Lockley [7,8] solved the problem for Clifford semigroups and idempotent semigroups, in [1] the author generalized their results to completely regular semigroups. Finally, Zhitomirskiy [19] studied the question for inverse semigroups.

ON E-UNITARY COVERS OF ORTHODOX SEMIGROUPS

1993 ◽  
Vol 03 (03) ◽  
pp. 317-333 ◽  
Author(s):  
MÁRIA B. SZENDREI
Keyword(s):  
Semidirect Product ◽  
Orthodox Semigroup ◽  
Regular Semigroups ◽  
Band Variety ◽  
Orthodox Semigroups

In this paper we prove that each orthodox semigroup S has an E-unitary cover embeddable into a semidirect product of a band B by a group where B belongs to the band variety generated by the band of idempotents in S. This result is related to an embeddability question on E-unitary regular semigroups raised previously.

scholarly journals On existence varieties of orthodox semigroups

1995 ◽  
Vol 58 (1) ◽  
pp. 100-125 ◽  
Author(s):  
J. Doyle
Keyword(s):  
Inverse Semigroups ◽  
Direct Products ◽  
Regular Semigroups ◽  
Existence Variety ◽  
Orthodox Semigroups

AbstractAn existence variety of regular semigroups is a class of regular semigroups which is closed under the operations of forming all homomorphic images, all regular subsemigroups and all direct products. In this paper we generalize results on varieties of inverse semigroups to existence varieties of orthodox semigroups.

ORTHODOX TRANSVERSALS OF REGULAR SEMIGROUPS

2001 ◽  
Vol 11 (02) ◽  
pp. 269-279 ◽  
Author(s):  
J. F. CHEN ◽  
Y. Q. CUO
Keyword(s):  
Regular Semigroups ◽  
Orthodox Semigroups

Orthodox transversals were introduced by the first author as a generalization of inverse transversals [Comm. Algebra 27(9) (1999), pp. 4275–4288]. One of our aims in this note is to consider the general case of orthodox transversals. The main results are on the sets I and Λ, two components of regular semigroups with orthodox transversals. We prove that the semibands Ī and [Formula: see text] generated by I and Λ respectively are bands. Also somewhat interesting generalizations of properties on orthodox semigroups are given; another aim in this note is to give some examples illustrating the situations that the class of regular semigroups with orthodox transversals properly includes the class of regular semigroups with inverse transversals as well as the class of orthodox semigroups.

scholarly journals On generalized Ehresmann semigroups

2017 ◽  
Vol 15 (1) ◽  
pp. 1132-1147
Author(s):  
Shoufeng Wang
Keyword(s):  
Inverse Semigroups ◽  
Inverse Transversal ◽  
Regular Semigroups ◽  
Admissible Triple ◽  
Orthodox Semigroups ◽  
Ehresmann Semigroups

Abstract As a generalization of the class of inverse semigroups, the class of Ehresmann semigroups is introduced by Lawson and investigated by many authors extensively in the literature. In particular, Gomes and Gould construct a fundamental Ehresmann semigroup CE from a semilattice E which plays for Ehresmann semigroups the role that TE plays for inverse semigroups, where TE is the Munn semigroup of a semilattice E. From a varietal perspective, Ehresmann semigroups are derived from reduction of inverse semigroups. In this paper, from varietal perspective Ehresmann semigroups are extended to generalized Ehresmann semigroups derived instead from normal orthodox semigroups (i.e. regular semigroups whose idempotents form normal bands) with an inverse transversal. We present here a semigroup C(I,Λ,E∘) from an admissible triple (I, Λ, E∘) that plays for generalized Ehresmann semigroups the role that CE from a semilattice E plays for Ehresmann semigroups. More precisely, we show that a semigroup is a fundamental generalized Ehresmann semigroup whose admissible triple is isomorphic to (I, Λ, E∘) if and only if it is (2,1,1,1)-isomorphic to a quasi-full (2,1,1,1)-subalgebra of C(I,Λ,E∘). Our results generalize and enrich some results of Fountain, Gomes and Gould on weakly E-hedges semigroups and Ehresmann semigroups.

Idempotent-equivalent congruences on orthodox semigroups

1970 ◽  
Vol 11 (2) ◽  
pp. 221-241 ◽  
Author(s):  
John Meakin
Keyword(s):  
Regular Semigroups ◽  
Orthodox Semigroups

Any congruence on a semigroup S with a nonempty set Es of idempotents induces a partition of the set Es. Two congruences ρ and σ on the semigroup S are defined to be idempotent-equivalent congruences on S if ρ and σ induce the same partition of Es. In this paper we investigate idempotent-equivalent congruences on orthodox semigroups (regular semigroups in which the set of idempotents forms a subsemigroup).

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