scholarly journals The pseudoidentity problem and reducibility for completely regular semigroups

2001 ◽  
Vol 63 (3) ◽  
pp. 407-433 ◽  
Author(s):  
Jorge Almedia ◽  
Peter G. Trotter
Keyword(s):  
Word Problem ◽  
Finite Groups ◽  
Open Problem ◽  
Sufficient Conditions ◽  
90Th Birthday ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Strengthened Version ◽  
Completely Regular Semigroups ◽  
Necessary And Sufficient

Dedicated to George Szekeres on the occasion of his 90th birthdayNecessary and sufficient conditions for equality over the pseudovariety CR of all finite completely regular semigroups are obtained. They are inspired by the solution of the word problem for free completely regular semigroups and clarify the role played by groups in the structure of such semigroups. A strengthened version of Ash's inevitability theorem (κ-reducibility of the pseudovariety G of all finite groups) is proposed as an open problem and it is shown that, if this stronger version holds, then CR is also κ-reducible and, therefore, hyperdecidable.

Completely Regular Semigroups with Generalized Strong Semilattice Decompositions

2005 ◽  
Vol 12 (02) ◽  
pp. 269-280 ◽  
Author(s):  
Xiangzhi Kong ◽  
K. P. Shum
Keyword(s):  
Sufficient Conditions ◽  
Normal Band ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Green’S Relation ◽  
Completely Regular Semigroups ◽  
Semilattice Of Semigroups ◽  
Strong Semilattice ◽  
Necessary And Sufficient ◽  
Characterization Theorems

The concept of ρG-strong semilattice of semigroups is introduced. By using this concept, we study Green's relation ℋ on a completely regular semigroup S. Necessary and sufficient conditions for S/ℋ to be a regular band or a right quasi-normal band are obtained. Important results of Petrich and Reilly on regular cryptic semigroups are generalized and enriched. In particular, characterization theorems of regular cryptogroups and normal cryptogroups are obtained.

scholarly journals Hyperdecidability of pseudovarieties of orthogroups

2001 ◽  
Vol 43 (1) ◽  
pp. 67-83 ◽  
Author(s):  
Jorge Almeida ◽  
Peter G. Trotter
Keyword(s):  
Word Problem ◽  
Weak Inversion ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Completely Regular Semigroups ◽  
Mal'cev Product ◽  
Mal’Cev Product

Let W denote the intersection with the pseudovariety of completely regular semigroups of the Mal'cev product of the pseudovariety of bands with a pseudovariety V of completely regular semigroups. It is shown that the (pseudo)word problem for W is reduced to that for V in such a way that decidability is preserved in the case in which terms involving only multiplication and weak inversion are considered. It is also shown that, if V is a hyperdecidable (respectively canonically reducible) pseudovariety of groups, then so is W.

PSEUDOVARIETY JOINS INVOLVING ${\mathscr J}$ -TRIVIAL SEMIGROUPS

1999 ◽  
Vol 09 (01) ◽  
pp. 99-112 ◽  
Author(s):  
JORGE ALMEIDA ◽  
ASSIS AZEVEDO ◽  
MARC ZEITOUN
Keyword(s):  
Finite Groups ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Completely Regular Semigroups

J. Rhodes asked during the Chico Conference in 1986 for the calculation of joins of semigroup pseudovarieties. This paper proves that the join J∨H of the pseudovariety J of [Formula: see text]-trivial semigroups and of any 2-strongly decidable pseudovariety V of of completely regular semigroups is decidable. This problem was proposed by the first author for V=G, the pseudovariety of finite groups.

scholarly journals Free completely regular semigroups II. Word problem

1983 ◽  
Vol 82 (1) ◽  
pp. 143-156 ◽  
Author(s):  
J.A Gerhard
Keyword(s):  
Word Problem ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Completely Regular Semigroups

On the word problem for free completely regular semigroups

1986 ◽  
Vol 34 (1) ◽  
pp. 127-138 ◽  
Author(s):  
Jiří Kadourek ◽  
Libor Polák
Keyword(s):  
Word Problem ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Completely 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).

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.

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.

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