A Munn tree type representation for the elements of the bifree locally inverse semigroup

2016 ◽  
Vol 183 (4) ◽  
pp. 653-678
Author(s):  
Luís Oliveira
Keyword(s):  
Inverse Semigroup ◽  
Type Representation ◽  
Locally Inverse Semigroup ◽  
Tree Type

REPRESENTATIONS OF LOCALLY INVERSE *-SEMIGROUPS

1996 ◽  
Vol 06 (05) ◽  
pp. 541-551
Author(s):  
TERUO IMAOKA ◽  
ISAMU INATA ◽  
HIROAKI YOKOYAMA
Keyword(s):  
Inverse Semigroup ◽  
Wreath Product ◽  
Representation Theorem ◽  
Generalized Inverse ◽  
Inverse Semigroups ◽  
Locally Inverse Semigroup ◽  
The One ◽  
Locally Inverse Semigroups ◽  
Generalized Inverse Semigroups

The first author obtained a generalization of Preston-Vagner Representation Theorem for generalized inverse *-semigroups. In this paper, we shall generalize their results for locally inverse *-semigroups. Firstly, by introducing a concept of a π-set (which is slightly different from the one in [7]), we shall construct the π-symmetric locally inverse *-semigroup on a π-set, and show that any locally inverse *-semigroup can be embedded up to *-isomorphism in the π-symmetric locally inverse semigroup on a π-set. Moreover, we shall obtain that the wreath product of locally inverse *-semigroups is also a locally inverse *-semigroup.

scholarly journals REES MATRIX COVERS FOR A CLASS OF SEMIGROUPS WITH LOCALLY COMMUTING IDEMPOTENTS

2001 ◽  
Vol 44 (1) ◽  
pp. 173-186 ◽  
Author(s):  
Tanveer A. Khan ◽  
Mark V. Lawson
Keyword(s):  
Inverse Semigroup ◽  
Subject Classification ◽  
Rees Matrix Semigroup ◽  
Primary 20M10 ◽  
Locally Inverse Semigroup ◽  
Matrix Semigroup

AbstractMcAlister proved that every regular locally inverse semigroup can be covered by a regular Rees matrix semigroup over an inverse semigroup by means of a homomorphism which is locally an isomorphism. We generalize this result to the class of semigroups with local units whose local submonoids have commuting idempotents and possessing what we term a ‘McAlister sandwich function’.AMS 2000 Mathematics subject classification: Primary 20M10. Secondary 20M17

scholarly journals On the Bifree Locally Inverse Semigroup

1995 ◽  
Vol 178 (2) ◽  
pp. 581-613 ◽  
Author(s):  
K. Auinger
Keyword(s):  
Inverse Semigroup ◽  
Locally Inverse Semigroup

Rees Matrix Covers and the Translational Hull of a Locally Inverse Semigroup

2008 ◽  
Vol 36 (9) ◽  
pp. 3230-3249 ◽  
Author(s):  
Francis J. Pastijn ◽  
Luís A. Oliveira
Keyword(s):  
Inverse Semigroup ◽  
Locally Inverse Semigroup

Ideal extensions of locally inverse semigroups

2008 ◽  
Vol 45 (3) ◽  
pp. 395-409 ◽  
Author(s):  
Francis Pastijn ◽  
Luís Oliveira
Keyword(s):  
Inverse Semigroup ◽  
Inverse Semigroups ◽  
Inverse Subsemigroup ◽  
Locally Inverse Semigroup ◽  
Locally Inverse Semigroups

The translational hull of a locally inverse semigroup has a largest locally inverse subsemigroup containing the inner part. A construction is given for ideal extensions within the class of all locally inverse semigroups.

scholarly journals A Note on Locally Inverse Semigroup Algebras

2008 ◽  
Vol 2008 ◽  
pp. 1-5 ◽  
Author(s):  
Xiaojiang Guo
Keyword(s):  
Inverse Semigroup ◽  
Commutative Ring ◽  
Direct Product ◽  
Necessary Conditions ◽  
Semigroup Algebra ◽  
Semigroup Algebras ◽  
Locally Inverse Semigroup ◽  
Maximum Subgroup ◽  
Sufficient And Necessary Conditions

LetRbe a commutative ring andSa finite locally inverse semigroup. It is proved that the semigroup algebraR[S]is isomorphic to the direct product of Munn algebrasℳ(R[GJ],mJ,nJ;PJ)withJ∈S/𝒥, wheremJis the number ofℛ-classes inJ,nJthe number ofℒ-classes inJ, andGJa maximum subgroup ofJ. As applications, we obtain the sufficient and necessary conditions for the semigroup algebra of a finite locally inverse semigroup to be semisimple.

ON LOCALLY EHRESMANN SEMIGROUPS

2011 ◽  
Vol 10 (06) ◽  
pp. 1165-1186 ◽  
Author(s):  
XUEMING REN ◽  
DANDAN YANG ◽  
K. P. SHUM
Keyword(s):  
Inverse Semigroup ◽  
Rees Matrix Semigroup ◽  
Locally Inverse Semigroup ◽  
Matrix Semigroup ◽  
Ehresmann Semigroups

It was first proved by McAlister in 1983 that every locally inverse semigroup is a locally isomorphic image of a regular Rees matrix semigroup over an inverse semigroup and Lawson in 2000 further generalized this result to some special locally adequate semigroups. In this paper, we show how these results can be extended to a class of locally Ehresmann semigroups.

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