TWO PARTICULAR EVENTUALLY REGULAR SEMIGROUPS WITH 0-MODULAR OR 0-DISTRIBUTIVE SUBSEMIGROUP LATTICES

2013 ◽  
Vol 06 (04) ◽  
pp. 1350046
Author(s):  
Yu Wang ◽  
Zhixiang Yin
Keyword(s):  
Inverse Semigroup ◽  
Regular Semigroup ◽  
Regular Semigroups ◽  
Subsemigroup Lattice

The structure of a completely π-regular semigroup with 0-modular or 0-distributive subsemigroup lattice is given. Furthermore, it is shown that an eventually inverse semigroup to have 0-modular or 0-distributive subsemigroup lattice is a completely π-regular semigroup which is a semilattice of completely archimedean semigroups. Thus the structure of an eventually inverse semigroup whose subsemigroup lattice is 0-modular or 0-distributive is characterized as well.

scholarly journals Epis are onto for finite regular semigroups

1983 ◽  
Vol 26 (2) ◽  
pp. 151-162 ◽  
Author(s):  
T. E. Hall ◽  
P. R. Jones
Keyword(s):  
Inverse Semigroup ◽  
Regular Semigroup ◽  
Open Problem ◽  
Inverse Semigroups ◽  
Regular Semigroups ◽  
Preliminary Results ◽  
Absolutely Closed ◽  
Finite Regular Semigroup

After preliminary results and definitions in Section 1, we show in Section 2 that any finite regular semigroup is saturated, in the sense of Howie and Isbell [8] (that is, the dominion of a finite regular semigroup U in a strictly containing semigroup S is never S). This is equivalent of course to showing that in the category of semigroups any epi from a finite regular semigroup is in fact onto. Note for inverse semigroups the stronger result, that any inverse semigroup is absolutely closed [11, Theorem VII. 2.14] or [8, Theorem 2.3]. Further, any inverse semigroup is in fact an amalgamation base in the class of semigroups [10], in the sense of [5]. These stronger results are known to be false for finite regular semigroups [8, Theorem 2.9] and [5, Theorem 25]. Whether or not every regular semigroup is saturated is an open problem.

scholarly journals The natural partial order on a regular semigroup

1980 ◽  
Vol 23 (3) ◽  
pp. 249-260 ◽  
Author(s):  
K. S. Subramonian Nambooripad
Keyword(s):  
Inverse Semigroup ◽  
Regular Semigroup ◽  
Partial Order ◽  
Inverse Semigroups ◽  
Natural Partial Order ◽  
Simple Description ◽  
Regular Semigroups ◽  
Simple Congruence ◽  
Pseudo Inverse ◽  
Completely Simple

It is well-known that on an inverse semigroup S the relation ≦ defined by a ≦ b if and only if aa−1 = ab−1 is a partial order (called the natural partial order) on S and that this relation is closely related to the global structure of S (cf. (1, §7.1), (10)). Our purpose here is to study a partial order on regular semigroups that coincides with the relation defined above on inverse semigroups. It is found that this relation has properties very similar to the properties of the natural partial order on inverse semigroups. However, this relation is not, in general, compatible with the multiplication in the semigroup. We show that this is true if and only if the semigroup is pseudo-inverse (cf. (8)). We also show how this relation may be used to obtain a simple description of the finest primitive congruence and the finest completely simple congruence on a regular semigroup.

scholarly journals SEMIGRUP REGULER DAN SIFAT-SIFATNYA

2021 ◽  
Vol 13 (2) ◽  
pp. 71
Author(s):  
Najmah Istikaanah ◽  
Ari Wardayani ◽  
Renny Renny ◽  
Ambar Sari Nurahmadhani ◽  
Agustini Tripena Br. Sb.
Keyword(s):  
Inverse Semigroup ◽  
Regular Semigroup ◽  
Cartesian Product ◽  
Regular Semigroups

This article discusses some properties of regular semigroups. These properties are especially concerned with the relation of the regular semigroups  to ideals, subsemigroups, groups, idempoten semigroups and invers semigroups. In addition,  this paper also discusses the Cartesian product of two regular semigroups.   Keywords:ideal, idempoten semigroup, inverse semigroup, regular semigroup, subsemigroup.

R-Unipotent Congruences on Eventually Regular Semigroups

2007 ◽  
Vol 14 (01) ◽  
pp. 37-52 ◽  
Author(s):  
Yanfeng Luo ◽  
Xiaoling Li
Keyword(s):  
Positive Integer ◽  
Inverse Semigroup ◽  
Regular Semigroup ◽  
Regular Semigroups ◽  
Normal Subsemigroup ◽  
Normal Congruence ◽  
Eventually Regular Semigroup

A semigroup S is called an eventually regular semigroup if for every a ∈ S, there exists a positive integer n such that an is regular. In this paper, the R-unipotent, inverse semigroup and group congruences on an eventually regular semigroup S are described by means of certain congruence pairs (ξ, K), where ξ is a normal congruence on the subsemigroup 〈E(S)〉 generated by E(S), and K is a normal subsemigroup of S.

scholarly journals Regular semigroups, fundamental semigroups and groups

1980 ◽  
Vol 29 (4) ◽  
pp. 475-503 ◽  
Author(s):  
D. B. McAlister
Keyword(s):  
Regular Semigroup ◽  
Partial Order ◽  
Direct Product ◽  
Homomorphic Image ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Natural Partial Order ◽  
Regular Semigroups ◽  
Necessary And Sufficient ◽  
Fundamental Semigroups

AbstractIn this paper we obtain necessary and sufficient conditions on a regular semigroup in order that it should be an idempotent separating homomorphic image of a full subsemigroup of the direct product of a group and a fundamental or combinatorial regular semigroup. The main tool used is the concept of a prehomomrphism θ: S → T between regular semigroups. This is a mapping such that (ab) θ ≦ aθ bθ in the natural partial order on T.

scholarly journals FACTORIZATION THEOREMS FOR MORPHISMS OF ORDERED GROUPOIDS AND INVERSE SEMIGROUPS

2001 ◽  
Vol 44 (3) ◽  
pp. 549-569 ◽  
Author(s):  
Benjamin Steinberg
Keyword(s):  
Inverse Semigroup ◽  
Regular Semigroup ◽  
Classical Theory ◽  
Derived Category ◽  
Inverse Semigroups ◽  
Subject Classification

AbstractAdapting the theory of the derived category to ordered groupoids, we prove that every ordered functor (and thus every inverse and regular semigroup homomorphism) factors as an enlargement followed by an ordered fibration. As an application, we obtain Lawson’s version of Ehresmann’s Maximum Enlargement Theorem, from which can be deduced the classical theory of idempotent-pure inverse semigroup homomorphisms and $E$-unitary inverse semigroups.AMS 2000 Mathematics subject classification: Primary 20M18; 20L05; 20M17

scholarly journals Enlargements of regular semigroups

1996 ◽  
Vol 39 (3) ◽  
pp. 425-460 ◽  
Author(s):  
M. V. Lawson
Keyword(s):  
Regular Semigroup ◽  
Semigroup Theory ◽  
Regular Semigroups

We introduce a class of regular extensions of regular semigroups, called enlargements; a regular semigroup T is said to be an enlargement of a regular subsemigroup S if S = STS and T = TST. We show that S and T have many properties in common, and that enlargements may be used to analyse a number of questions in regular semigroup theory.

scholarly journals A special sublattice of the congruence lattice of a regular semigroup

1997 ◽  
Vol 40 (3) ◽  
pp. 457-472 ◽  
Author(s):  
Mario Petrich
Keyword(s):  
Distributive Lattice ◽  
Regular Semigroup ◽  
Congruence Lattice ◽  
Regular Semigroups ◽  
Generators And Relations ◽  
Completely Regular ◽  
Completely Simple Semigroups ◽  
Special Cases ◽  
Completely Regular Semigroups ◽  
Completely Simple

Let S be a regular semigroup and be its congruence lattice. For ρ ∈ , we consider the sublattice Lρ of generated by the congruences pw where w ∈ {K, k, T, t}* and w has no subword of the form KT, TK, kt, tk. Here K, k, T, t are the operators on induced by the kernel and the trace relations on . We find explicitly the least lattice L whose homomorphic image is Lρ for all ρ ∈ and represent it as a distributive lattice in terms of generators and relations. We also consider special cases: bands of groups, E-unitary regular semigroups, completely simple semigroups, rectangular groups as well as varieties of completely regular semigroups.

REGULAR SEMIGROUPS WITH NORMAL IDEMPOTENTS

2017 ◽  
Vol 103 (1) ◽  
pp. 116-125
Author(s):  
XIANGFEI NI ◽  
HAIZHOU CHAO
Keyword(s):  
Regular Semigroup ◽  
Simple Method ◽  
Regular Semigroups

In this paper, we investigate regular semigroups that possess a normal idempotent. First, we construct a nonorthodox nonidempotent-generated regular semigroup which has a normal idempotent. Furthermore, normal idempotents are described in several different ways and their properties are discussed. These results enable us to provide conditions under which a regular semigroup having a normal idempotent must be orthodox. Finally, we obtain a simple method for constructing all regular semigroups that contain a normal idempotent.

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.

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