Regular semigroups

1978 ◽  
Vol 16 (1) ◽  
pp. 369-377 ◽  
Author(s):  
T. E. Nordahl ◽  
H. E. Scheiblich
Keyword(s):  
Regular Semigroups

scholarly journals On the lattice of varieties of completely regular semigroups

1983 ◽  
Vol 35 (2) ◽  
pp. 227-235 ◽  
Author(s):  
P. R. Jones
Keyword(s):  
Lattice Of Varieties ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Variety Of Groups ◽  
Completely Regular Semigroups ◽  
Subdirect Products

AbstractSeveral morphisms of this lattice V(CR) are found, leading to decompostions of it, and various sublattices, into subdirect products of interval sublattices. For example the map V → V ∪ G (where G is the variety of groups) is shown to be a retraction of V(CR); from modularity of the lattice V(BG) of varieties of bands of groups it follows that the map V → (V ∪ V V G) is an isomorphism of V(BG).

Regular Semigroups with Quasi-Ideal Orthodox Transversals

2007 ◽  
Vol 74 (2) ◽  
pp. 247-258 ◽  
Author(s):  
Xiangjun Kong
Keyword(s):  
Regular Semigroups

scholarly journals Arbitrary vs. regular semigroups

1984 ◽  
Vol 34 (1) ◽  
pp. 57-115 ◽  
Author(s):  
Jean-Camille Birget
Keyword(s):  
Regular Semigroups

Congruences on ideal nil-extension of completely regular semigroups

1998 ◽  
Vol 43 (5) ◽  
pp. 379-381
Author(s):  
Xueming Ren ◽  
Yuqi Guo ◽  
Jiaping Cen
Keyword(s):  
Regular Semigroups ◽  
Completely Regular ◽  
Completely Regular Semigroups ◽  
Nil Extension

scholarly journals Eventually regular semigroups that are group-bound

1986 ◽  
Vol 34 (1) ◽  
pp. 127-132 ◽  
Author(s):  
P. M. Edwards
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Regular Semigroups ◽  
Necessary And Sufficient

Necessary and sufficient conditions are given for certain classes of eventually regular semigroups to the group-bound or even periodic.

Congruence-free regular semigroups with zero

1976 ◽  
Vol 12 (1) ◽  
pp. 1-5 ◽  
Author(s):  
P. G. Trotter
Keyword(s):  
Regular Semigroups

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 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.

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