On a class of Dubreil-Jacotin regular semigroups and a construction of Yamada

1977 ◽  
Vol 77 (1-2) ◽  
pp. 145-150 ◽  
Author(s):  
T. S. Blyth
Keyword(s):  
Structure Theorem ◽  
Present Approach ◽  
Inverse Semigroups ◽  
Regular Semigroups ◽  
Structure Theorems

SynopsisIn the publication [2] we obtained some structure theorems for certain Dubreil-Jacotin regular semigroups. A crucial observation in the course of investigating these types of ordered regular semigroups was that the (ordered) band of idempotents was normal. This is characteristic of a class of semigroups studied by Yamada [5] and called generalised inverse semigroups. Here we specialise a construction of Yamada to obtain a structure theorem that complements those in [2], The important feature of the present approach is the part played by the greatest elements that exist in each of the components in the semilattice decompositions involved.

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.

Inverse semigroups generated by a pair of subgroups

1977 ◽  
Vol 77 (1-2) ◽  
pp. 9-22 ◽  
Author(s):  
D. B. McAlister
Keyword(s):  
Inverse Semigroup ◽  
Free Product ◽  
Homomorphic Image ◽  
Main Part ◽  
Structure Theorem ◽  
Inverse Semigroups ◽  
Infinite Cyclic Group ◽  
The Third ◽  
Group A ◽  
Maximum Group

SynopsisThe aim of this paper is to describe the free product of a pair G, H of groups in the category of inverse semigroups. Since any inverse semigroup generated by G and H is a homomorphic image of this semigroup, this paper can be regarded as asking how large a subcategory, of the category of inverse semigroups, is the category of groups? In this light, we show that every countable inverse semigroup is a homomorphic image of an inverse subsemigroup of the free product of two copies of the infinite cyclic group. A similar result can be obtained for arbitrary cardinalities. Hence, the category of inverse semigroups is generated, using algebraic constructions by the subcategory of groups.The main part of the paper is concerned with obtaining the structure of the free product G inv H, of two groups G, H in the category of inverse semigroups. It is shown in section 1 that G inv H is E-unitary; thus G inv H can be described in terms of its maximum group homomorphic image G gp H, the free product of G and H in the category of groups, and its semilattice of idempotents. The second section considers some properties of the semilattice of idempotents while the third applies these to obtain a representation of G inv H which is faithful except when one group is a non-trivial finite group and the other is trivial. This representation is used in section 4 to give a structure theorem for G inv H. In this section, too, the result described in the first paragraph is proved. The last section, section 5, consists of examples.

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.

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 Congruences and Green's relations on regular semigroups

1972 ◽  
Vol 13 (2) ◽  
pp. 167-175 ◽  
Author(s):  
T. E. Hall
Keyword(s):  
Generalized Inverse ◽  
Inverse Semigroups ◽  
Green’S Relations ◽  
Regular Semigroups ◽  
Green's Relations ◽  
Generalized Inverse Semigroups

It is sometimes possible to reconstruct semigroups from some of their homomorphic images. Some recent examples have been the construction of bisimple inverse semigroups from fundamental bisimple inverse semigroups [9], and the construction of generalized inverse semigroups from inverse semigroups [12].

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.

scholarly journals Inverse semigroups with zero: covers and their structure

1999 ◽  
Vol 67 (1) ◽  
pp. 15-30 ◽  
Author(s):  
Sydney Bulman-Fleming ◽  
John Fountain ◽  
Victoria Gould
Keyword(s):  
Inverse Image ◽  
Inverse Semigroups ◽  
Structure Theorems ◽  
The Many

AbstractWe obtain analogues, in the setting of semigroups with zero, of McAlister's convering theoren and the structure theorems of McAlister, O'Carroll, and Margolis and Pin. The covers come from a class C of semigroups defined by modifying one of the many characterisations of E-unitary inverse semigroups, namely, that an inverse semigroups is E-unitary if and only if it is an inverse image of an idempotent-pure homomorphism onto a group. The class C is properly contained in the class of all E*-unitary inverse semigroups introduced by Szendrei but properly contains the class of strongly categorical E*-unitary semigroups recently considered by Gomes and Howie.

Structure theorems for regular semigroups

1972 ◽  
Vol 4 (1) ◽  
pp. 95-123 ◽  
Author(s):  
Gerard Lallement
Keyword(s):  
Regular Semigroups ◽  
Structure Theorems
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