Semigroup Forum

, Volume 96, Issue 2, pp 348–356 | Cite as

On pseudo-amenability of commutative semigroup algebras and their second duals

  • M. Soroushmehr
  • M. Rostami
  • M. Essmaili
Research Article


In this paper, we first characterize pseudo-amenability of semigroup algebras \(\ell ^1(S),\) for a certain class of commutative semigroups S,  the so-called archimedean semigroups. We show that for an archimedean semigroup S,  pseudo-amenability, amenability and approximate amenability of \(\ell ^1(S)\) are equivalent. Then for a commutative semigroup S,  we show that pseudo-amenability of \(\ell ^{1}(S)\) implies that S is a Clifford semigroup. Finally, we give some results on pseudo-amenability and approximate amenability of the second dual of a certain class of commutative semigroup algebras \(\ell ^1(S)\).


Pseudo-amenability Approximate amenability Archimedean semigroup Clifford semigroup Commutative semigroup Semigroup algebra 



The authors thank the referee for his/her invaluable comments and suggestions. The first author was supported by Grant No. 95004213 from Iran National Science Foundation which is gratefully acknowledged.


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Mosaheb Institue of MathematicsKharazmi UniversityTehranIran
  2. 2.Faculty of Mathematical and Computer ScienceAmirkabir University of TechnologyTehranIran
  3. 3.Faculty of Mathematical and Computer SciencesKharazmi UniversityTehranIran

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