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

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.

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.

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.

scholarly journals Module amenability of restricted semigroup algebras under module actions

Filomat ◽  
2015 ◽  
Vol 29 (4) ◽  
pp. 787-793
Author(s):  
Abbas Sahleh ◽  
Somaye Tanha
Keyword(s):  
Inverse Semigroup ◽  
Semigroup Algebra ◽  
Semigroup Algebras ◽  
Clifford Semigroup ◽  
Module Amenability

In this article, weshow that module amenability with the canonical action of restricted semigroup algebra l1r (S) and semigroup algebra l1(Sr) are equivalent, where Sr is the restricted semigroup of associated to the inverse semigroup S. We use this to give a characterization of module amenability of restricted semigroup algebra l1r (S) with the canonical action, where S is a Clifford semigroup.

scholarly journals A groupoid approach to discrete inverse semigroup algebras

2010 ◽  
Vol 223 (2) ◽  
pp. 689-727 ◽  
Author(s):  
Benjamin Steinberg
Keyword(s):  
Inverse Semigroup ◽  
Semigroup Algebras

Second module cohomology group of inverse semigroup algebras

2010 ◽  
Vol 81 (2) ◽  
pp. 269-276 ◽  
Author(s):  
E. Nasrabadi ◽  
A. Pourabbas
Keyword(s):  
Inverse Semigroup ◽  
Cohomology Group ◽  
Semigroup Algebras

Semiprimitivity of inverse semigroup algebras

1982 ◽  
Vol 93 (1-2) ◽  
pp. 83-98 ◽  
Author(s):  
W. D. Munn
Keyword(s):  
Inverse Semigroup ◽  
Group Algebras ◽  
Prime Characteristic ◽  
Semigroup Algebras ◽  
Completely Semisimple

SynopsisLet S be an inverse semigroup and F a field. It is shown that if F has characteristic 0 and is not algebraic over its prime subfield then the algebra of S over F is semiprimitive (i.e. Jacobson semisimple). This generalises a well-known theorem on group algebras due to Amitsur. Similar results for the case in which F has prime characteristic are obtained under the additional hypotheses that S is completely semisimple or that S is E-unitary with a totally ordered semilattice.

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