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 Eventually Pointed Principally Ordered Regular Semigroups

2020 ◽  
Vol 24 (2) ◽  
pp. 139
Author(s):  
G.A. Pinto
Keyword(s):  
Positive Integer ◽  
Regular Semigroup ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Regular Semigroups ◽  
Necessary And Sufficient ◽  
Completely Simple

An ordered regular semigroup, , is said to be principally ordered if for every  there exists . A principally ordered regular semigroup is pointed if for every element,  we have . Here we investigate those principally ordered regular semigroups that are eventually pointed in the sense that for all  there exists a positive integer, , such that . Necessary and sufficient conditions for an eventually pointed principally ordered regular semigroup to be naturally ordered and to be completely simple are obtained. We describe the subalgebra of  generated by a pair of comparable idempotents  and such that . 

scholarly journals Group congruences on eventually regular semigroups

1988 ◽  
Vol 45 (3) ◽  
pp. 320-325 ◽  
Author(s):  
S. Hanumantha Rao ◽  
P. Lakshmi
Keyword(s):  
Regular Semigroup ◽  
Group Congruence ◽  
Regular Semigroups ◽  
Eventually Regular Semigroup ◽  
Lattice Of Congruences

AbstractA characterization of group congruences on an eventually regular semigroup S is provided. It is shown that a group congruence is dually right modular in the lattice of congruences on S. Also for any group congruence ℸ and any congruence p on S, ℸ Vp and kernel ℸ Vp are described.

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 Minimum Group Congruences on Eventually Regular Semigroups

ISRN Algebra ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-5
Author(s):  
Wang Yu ◽  
Yin ZhiXiang
Keyword(s):  
Regular Semigroup ◽  
Group Congruence ◽  
Regular Semigroups ◽  
Minimum Group ◽  
Eventually Regular Semigroup

An eventually regular semigroup is a semigroup in which some power of any element is regular. The minimum group congruence on an eventually regular semigroup is investigated by means of weak inverse. Furthermore, some properties of the minimum group congruence on an eventually regular semigroup are characterized.

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 Congruences and Green's relations on eventually regular semigroups

1987 ◽  
Vol 43 (1) ◽  
pp. 64-69 ◽  
Author(s):  
P. M. Edwards ◽  
T. E. Hall
Keyword(s):  
Regular Semigroup ◽  
Green’S Relations ◽  
Regular Semigroups ◽  
Regular Elements ◽  
Green's Relations ◽  
Eventually Regular Semigroup

AbstractA semigroup is eventually regular if each of its elements has some power that is regular. Let 𝓚 be one of Green's relations and let ρ be a congruence on an eventually regular semigroup S. It is shown for 𝓚 = 𝓛, 𝓡 and 𝓓 that if A and B are regular elements of S/ρ that are 𝓚-related in S/ρ then there exist elements a ∈ A, b ∈ B such that a and b are 𝓚-related in S. The result is not true for 𝓗 or 𝓙.

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.

Certain congruences on eventually regular semigroups I

2015 ◽  
Vol 52 (4) ◽  
pp. 434-449
Author(s):  
Roman S. Gigoń
Keyword(s):  
Regular Semigroup ◽  
Orthodox Semigroup ◽  
Full Description ◽  
Clifford Semigroup ◽  
Regular Semigroups ◽  
Subdirect Products ◽  
Eventually Regular Semigroup

A semigroup is called eventually regular if each of its elements has a regular power. In this paper we study certain fundamental congruences on an eventually regular semigroup. We generalize some results of Howie and Lallement (1966) and LaTorre (1983). In particular, we give a full description of the semilattice of group congruences (together with the least such a congruence) on an arbitrary eventually regular (orthodox) semigroup. Moreover, we investigate UBG-congruences on an eventually regular semigroup. Finally, we study the eventually regular subdirect products of an E-unitary semigroup and a Clifford semigroup.

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 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.

Sign in / Sign up

Export Citation Format

Share Document