Semigroup Forum

, Volume 86, Issue 2, pp 279–288

Super module amenability of inverse semigroup algebras

RESEARCH ARTICLE

DOI: 10.1007/s00233-012-9432-0

Cite this article as:
Lashkarizadeh Bami, M., Valaei, M. & Amini, M. Semigroup Forum (2013) 86: 279. doi:10.1007/s00233-012-9432-0

Abstract

In this paper we compare the notions of super amenability and super module amenability of Banach algebras, which are Banach modules over another Banach algebra with compatible actions. We find conditions for the two notions to be equivalent. In particular, we study arbitrary module actions of l1(ES) on l1(S) for an inverse semigroup S with the set of idempotents ES and show that under certain conditions, l1(S) is super module amenable if and only if S is finite. We also study the super module amenability of l1(S)∗∗ and module biprojectivity of l1(S), for arbitrary actions.

Keywords

Module Arense regularModule biprojectiveModule derivationSuper module amenable

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IsfahanIsfahanIran
  2. 2.Department of Mathematics, Faculty of Mathematical SciencesTarbiat Modares UniversityTehranIran
  3. 3.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran