The $$\pi $$ π -Semisimplicity of Locally Inverse Semigroup Algebras

2019 ◽  
Vol 45 (5) ◽  
pp. 1323-1338
Author(s):  
Yingdan Ji
Keyword(s):  
Inverse Semigroup ◽  
Semigroup Algebras ◽  
Locally Inverse Semigroup

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.

Spectra in Some Inverse Semigroup Algebras

2004 ◽  
Vol 104 (2) ◽  
pp. 211-218 ◽  
Author(s):  
M. J. Crabb ◽  
J. Duncan ◽  
C. M. McGregor
Keyword(s):  
Inverse Semigroup ◽  
Semigroup Algebras

THE FIRST COHOMOLOGY GROUP OF BANACH INVERSE SEMIGROUP ALGEBRAS WITH COEFFICIENTS IN -EMBEDDED BANACH BIMODULES

2019 ◽  
Vol 101 (3) ◽  
pp. 488-495
Author(s):  
HOGER GHAHRAMANI
Keyword(s):  
Banach Space ◽  
Inverse Semigroup ◽  
Cohomology Group ◽  
Semigroup Algebra ◽  
Semigroup Algebras ◽  
Mild Conditions ◽  
First Cohomology Group

Let $S$ be a discrete inverse semigroup, $l^{1}(S)$ the Banach semigroup algebra on $S$ and $\mathbb{X}$ a Banach $l^{1}(S)$-bimodule which is an $L$-embedded Banach space. We show that under some mild conditions ${\mathcal{H}}^{1}(l^{1}(S),\mathbb{X})=0$. We also provide an application of the main result.

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 Moore-Penrose inversion in complex contracted inverse semigroup algebras

1999 ◽  
Vol 66 (3) ◽  
pp. 297-302
Author(s):  
W. D. Munn
Keyword(s):  
Inverse Semigroup ◽  
Group Algebra ◽  
Semigroup Algebra ◽  
Semigroup Algebras ◽  
Locally Finite ◽  
Complex Group ◽  
Complex Group Algebra

AbstractIt is shown that every element of the complex contracted semigroup algebra of an inverse semigroup S = S0 has a Moore-Penrose inverse, with respect to the natural involution, if and only if S is locally finite. In particular, every element of a complex group algebra has such an inverse if and only if the group is locally finite.

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

Trace functions on the algebras of certain E-unitary inverse semigroups

1995 ◽  
Vol 125 (5) ◽  
pp. 1077-1084 ◽  
Author(s):  
M. J. Crabb ◽  
W. D. Munn
Keyword(s):  
Inverse Semigroup ◽  
Semigroup Algebra ◽  
Inverse Semigroups ◽  
Trace Function ◽  
Complex Field ◽  
Semigroup Algebras ◽  
Complex Conjugation ◽  
Arbitrary Rank

A construction is given for a trace function on the semigroup algebra of a certain type of E-unitary inverse semigroup over any subfield of the complex field that is closed under complex conjugation. In particular, the method applies to the semigroup algebras of free inverse semigroups of arbitrary rank.

On the singular ideals of inverse semigroup algebras

1983 ◽  
Vol 26 (1) ◽  
pp. 375-377 ◽  
Author(s):  
W. D. Munn
Keyword(s):  
Inverse Semigroup ◽  
Semigroup Algebras
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