Embedding semirings by translational hulls

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

The Translational Hull of a Semilattice of Weakly Reductive Semigroups

1974 ◽  
Vol 26 (6) ◽  
pp. 1520-1536
Author(s):  
Mario Petrich
Keyword(s):  
Explicit Form ◽  
Inverse Limit ◽  
Central Importance ◽  
Translational Hulls ◽  
Special Classes

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.

Translational hulls and block designs

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

scholarly journals Translational hulls of polynomially related semigroups

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

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.

scholarly journals A characterization of translational hulls of a strongly right type B semigroup

2019 ◽  
Vol 17 (1) ◽  
pp. 1340-1349 ◽  
Author(s):  
Chunhua Li ◽  
Baogen Xu
Keyword(s):  
New York ◽  
Inverse Semigroups ◽  
Type B ◽  
Translational Hulls

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.

The Translational Hull of an Inverse Semigroup

1974 ◽  
Vol 26 (5) ◽  
pp. 1050-1068 ◽  
Author(s):  
N. R. Reilly
Keyword(s):  
Inverse Semigroup ◽  
Direct Product ◽  
Left Translation ◽  
Composition Of Functions ◽  
Translational Hulls

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.

scholarly journals On translational hulls of type-A semigroups

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