Semigroup Forum

, Volume 86, Issue 2, pp 279–288 | Cite as

Super module amenability of inverse semigroup algebras

RESEARCH ARTICLE

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 l 1(E S ) on l 1(S) for an inverse semigroup S with the set of idempotents E S and show that under certain conditions, l 1(S) is super module amenable if and only if S is finite. We also study the super module amenability of l 1(S)∗∗ and module biprojectivity of l 1(S), for arbitrary actions.

Keywords

Module Arense regular Module biprojective Module derivation Super module amenable 

Notes

Acknowledgements

The authors would like to thank the referee for careful reading. We are grateful to the office of graduate studies of the University of Isfahan for their support.

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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

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