Semigroup Forum

, Volume 86, Issue 2, pp 279-288

First online:

Super module amenability of inverse semigroup algebras

  • M. Lashkarizadeh BamiAffiliated withDepartment of Mathematics, University of Isfahan
  • , M. ValaeiAffiliated withDepartment of Mathematics, University of Isfahan Email author 
  • , M. AminiAffiliated withDepartment of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares UniversitySchool of Mathematics, Institute for Research in Fundamental Sciences (IPM)

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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.


Module Arense regular Module biprojective Module derivation Super module amenable