translational hulls
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2019 ◽  
Vol 17 (1) ◽  
pp. 1340-1349 ◽  
Author(s):  
Chunhua Li ◽  
Baogen Xu

Abstract The aim of this paper is to study the translational hull of a strongly right type B semigroup. Our main result is to prove that the translational hull of a strongly right type B semigroup is itself a strongly right type B semigroup. As an application, we give a proof of a problem posted by Petrich on translational hulls of inverse semigroups in Petrich (Inverse Semigroups, Wiley, New York, 1984) to the cases of some strongly right type B semigroups.


2011 ◽  
Vol 90 (2) ◽  
pp. 271-287 ◽  
Author(s):  
MARIO PETRICH

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.


2003 ◽  
Vol 269 (1) ◽  
pp. 240-249 ◽  
Author(s):  
Xiaojiang Guo ◽  
K.P. Shum
Keyword(s):  
Type A ◽  

1983 ◽  
Vol 27 (1) ◽  
pp. 247-263 ◽  
Author(s):  
Stuart W. Margolis ◽  
Jeffrey H. Dinitz

1983 ◽  
Vol 33 (1) ◽  
pp. 95-100 ◽  
Author(s):  
Matthew Gould ◽  
Raymond E. Richardson
Keyword(s):  

1977 ◽  
Vol 14 (1) ◽  
pp. 235-246 ◽  
Author(s):  
H. J. Weinert ◽  
R. D. Griepentrog
Keyword(s):  

1974 ◽  
Vol 26 (6) ◽  
pp. 1520-1536
Author(s):  
Mario Petrich

The translational hull is of central importance in the construction of ideal extensions and the study of densely embedded ideals particularly for weakly reductive semigroups (see [4, Chapter III]). The translational hull of semigroups belonging to a few special classes is known in an explicit form, and for some other classes of semigroups, certain properties of their translational hulls have been established (see [4, Chapter V]). We have generalized in [5] the concept of an inverse limit of groups in order to give a construction of the translational hull of a semigroup which is a semilattice of groups.


1974 ◽  
Vol 26 (5) ◽  
pp. 1050-1068 ◽  
Author(s):  
N. R. Reilly

Let S be a semigroup. A function λ(ρ) on S is a left (right) translation of S if, for all x, y ∊ S, λ(xy) = λ(x)y ((xy)ρ= x(yρ)). A left translation λ and a right translation ρ are said to be linked if x(λy) = (xρ)y, for all x,y ∊ S,and then the ordered pair (λ, ρ) is called a bitranslation. Clearly the set Λ(S) (P(S)) of all left (right) translations is a semigroup with respect to composition of functions. The set of bitranslations forms a subsemigroup of the direct product Λ(S) × P(S)which is called the translational hull, Ω(S), of S. A valuable survey of results relating to Ω(S) and its importance in relation to semigroup extensions will be found in Petrich's review [6], to which the reader is referred for basic results on translational hulls.


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