scholarly journals Abundant Rees matrix semigroups

1987 ◽  
Vol 42 (1) ◽  
pp. 132-142 ◽  
Author(s):  
M. V. Lawson
Keyword(s):  
Regular Semigroups ◽  
Rees Matrix Semigroups ◽  
Abundant Semigroups ◽  
Multiplicative Semigroups ◽  
Matrix Semigroups ◽  
Cancellative Monoids

AbstractThe class of abundant semigroups originally arose from ‘homological’ considerations in the theory of S-systems: they are the semigroup theoretic counterparts of PP-rings. Cancellative monoids, full subsemigroups of regular semigroups as well as the multiplicative semigroups of PP-rings are abundant. In this paper we investigate the properties of Rees matrix semigroups over abundant semigroups. Some of our results generalise McAlister's work on regular Rees matrix semigroups.

Rees matrix covers for a class of abundant semigroups

1987 ◽  
Vol 107 (1-2) ◽  
pp. 109-120
Author(s):  
Mark V. Lawson
Keyword(s):  
Inverse Semigroup ◽  
Structure Theory ◽  
Regular Semigroups ◽  
Rees Matrix Semigroups ◽  
Abundant Semigroups ◽  
Multiplicative Semigroups ◽  
Matrix Semigroups ◽  
Cancellative Monoids

SynopsisRecently considerable attention has been paid to the study of locally inverse regular semigroups. McAlister [14] obtained a description of such semigroups as locally isomorphic images of regular Rees matrix semigroups over an inverse semigroup. The class of abundant semigroups originally arose from ‘homological’ considerations in the theory of S-systems: they are the semigroup theoretic analogue of PP-rings. Cancellative monoids, full subsemigroups of regular semigroups as well as the multiplicative semigroups of PP rings are abundant. The aim of this paper is to show how the structure theory described above for regular semigroups may be generalised to a class of abundant semigroups.

scholarly journals Flows on Classes of Regular Semigroups and Cauchy Categories

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Suha Ahmed Wazzan
Keyword(s):  
General Structure ◽  
Transformation Semigroups ◽  
Full Transformation ◽  
Regular Semigroups ◽  
Rees Matrix Semigroups ◽  
Completely Simple Semigroups ◽  
Special Case ◽  
Brandt Semigroups ◽  
Matrix Semigroups ◽  
Completely Simple

We consider the structure of the flow monoid for some classes of regular semigroups (which are special case of flows on categories) and for Cauchy categories. In detail, we characterize flows for Rees matrix semigroups, rectangular bands, and full transformation semigroups and also describe the Cauchy categories for some classes of regular semigroups such as completely simple semigroups, Brandt semigroups, and rectangular bands. In fact, we obtain a general structure for the flow monoids on Cauchy categories.

scholarly journals COMPLETELY REGULAR MONOIDS WITH TWO GENERATORS

2011 ◽  
Vol 90 (2) ◽  
pp. 271-287 ◽  
Author(s):  
MARIO PETRICH
Keyword(s):  
Infinite Number ◽  
Free Semigroup ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Rees Matrix Semigroups ◽  
Completely Regular Semigroups ◽  
Special Case ◽  
Matrix Semigroups ◽  
Translational Hulls

AbstractWe classify semigroups in the title according to whether they have a finite or an infinite number ofℒ-classes or ℛ-classes. For each case, we provide a concrete construction using Rees matrix semigroups and their translational hulls. An appropriate relatively free semigroup is used to complete the classification. All this is achieved by first treating the special case in which one of the generators is idempotent. We conclude by a discussion of a possible classification of 2-generator completely regular semigroups.

Rees matrix semigroups over inverse semigroups

1986 ◽  
Vol 102 (1-2) ◽  
pp. 61-90 ◽  
Author(s):  
F. J. Pastijn ◽  
Mario Petrich
Keyword(s):  
Inverse Semigroup ◽  
Homomorphic Image ◽  
Inverse Semigroups ◽  
Rees Matrix Semigroup ◽  
Regular Semigroups ◽  
Rees Matrix Semigroups ◽  
Special Cases ◽  
Matrix Semigroup ◽  
Matrix Semigroups ◽  
Completely Simple

SynopsisA Rees matrix semigroup over an inverse semigroup contains a greatest regular subsemigroup. The regular semigroups obtained in this manner are abstractly characterized here. The greatest completely simple homomorphic image and the idempotent generated part of such semigroups are investigated. Rectangular bands of semilattices of groups and some special cases are characterized in several ways.

scholarly journals The characterization and the product of quasi-Ehresmann transversals

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 2051-2060
Author(s):  
Xiangjun Kong ◽  
Pei Wang
Keyword(s):  
Abundant Semigroup ◽  
Regular Semigroups ◽  
The Real ◽  
Abundant Semigroups

Wang (Filomat 29(5), 985-1005, 2015) introduced and investigated quasi-Ehresmann transversals of semi-abundant semigroups satisfy conditions (CR) and (CL) as the generalizations of orthodox transversals of regular semigroups in the semi-abundant case. In this paper, we give two characterizations for a generalized quasi-Ehresmann transversal to be a quasi-Ehresmann transversal. These results further demonstrate that quasi-Ehresmann transversals are the ?real? generalizations of orthodox transversals in the semi-abundant case. Moreover, we obtain the main result that the product of any two quasi-ideal quasi-Ehresmann transversals of a semi-abundant semigroup S which satisfy the certain conditions is a quasi-ideal quasi-Ehresmann transversal of S.

scholarly journals Semi-abundant semigroups with quasi-Ehresmann transversals

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 985-1005
Author(s):  
Shoufeng Wang
Keyword(s):  
Structure Theorem ◽  
Regular Semigroups ◽  
Abundant Semigroups

Chen (Communications in Algebra 27(2), 4275-4288, 1999) introduced and investigated orthodox 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 regular semigroups. Some interesting properties associated with quasi-Ehresmann transversals are established. Moreover, a structure theorem of semi-abundant semigroups with generalized bi-ideal strong quasi-Ehresmann transversals is obtained. Our results generalize and enrich Chen?s results.

scholarly journals On bisimple semigroups generated by a finite number of idempotents

1982 ◽  
Vol 33 (1) ◽  
pp. 92-101 ◽  
Author(s):  
Karl Byleen
Keyword(s):  
Finite Number ◽  
Partial Order ◽  
Natural Partial Order ◽  
Rees Matrix Semigroups ◽  
Matrix Semigroups ◽  
Completely Simple

AbstractNon-completely simple bisimple semigroups S which are generated by a finite number of idempotents are studied by means of Rees matrix semigroups over local submonoids eSe, e = e2 ∈ S. If under the natural partial order on the set Es of idempotents of such a semigroup S the sets ω(e) = {ƒ ∈ Es: ƒ ≤ e} for each e ∈ Es are well-ordered, then S is shown to contain a subsemigroup isomorphic to Sp4, the fundamental four-spiral semigroup. A non-completely simple hisimple semigroup is constructed which is generated by 5 idempotents but which does not contain a subsemigroup isomorphic to Sp4.

scholarly journals Generators and relations of Rees matrix semigroups

1999 ◽  
Vol 42 (3) ◽  
pp. 481-495 ◽  
Author(s):  
H. Ayik ◽  
N. Ruškuc
Keyword(s):  
Rees Matrix Semigroup ◽  
Finitely Generated ◽  
Finite Generation ◽  
Generators And Relations ◽  
Rees Matrix Semigroups ◽  
Finite Presentability ◽  
Matrix Semigroup ◽  
Finitely Presented ◽  
Matrix Semigroups ◽  
The Ideal

In this paper we consider finite generation and finite presentability of Rees matrix semigroups (with or without zero) over arbitrary semigroups. The main result states that a Rees matrix semigroup M[S; I, J; P] is finitely generated (respectively, finitely presented) if and only if S is finitely generated (respectively, finitely presented), and the sets I, J and S\U are finite, where U is the ideal of S generated by the entries of P.

Certain rees matrix semigroups with universal properties

1981 ◽  
Vol 22 (1) ◽  
pp. 101-118 ◽  
Author(s):  
Mario Petrich ◽  
Norman R. Reilly
Keyword(s):  
Rees Matrix Semigroups ◽  
Universal Properties ◽  
Matrix Semigroups

KNITTED SEMILATTIC STRUCTURE OF REGULAR ${\cal H}^\dag$-CYBER GROUPS

2011 ◽  
Vol 04 (03) ◽  
pp. 545-557
Author(s):  
Yu Su ◽  
Xiangzhi Kong
Keyword(s):  
Recent Result ◽  
Classical Theorem ◽  
Regular Semigroups ◽  
Abundant Semigroups ◽  
Structure Theorems ◽  
Semilattice Of Semigroups ◽  
Normal Formula

We consider regular [Formula: see text]-cyber groups in the class of [Formula: see text]-abundant semigroups. By using knitted semilattice of semigroups, we give some structure theorems for regular [Formula: see text]-cyber groups, right quasi-normal [Formula: see text]-cyber groups and normal [Formula: see text]-cyber groups. Our main result generalizes a classical theorem of Petrich- Reilly on normal cryptic groups from the class of regular semigroups to the class of generalized abundant semigroups and also entriches a recent result of Guo-Shum on left cyber groups.

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