Preprint Article Version 1 NOT YET PEER-REVIEWED

Amenability Modulo an Ideal of Second Duals of Semigroup Algebras

  1. Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, P. O. Box 13185/768 Tehran, Iran
  2. Department of Mathematics, Science and Research Branch, Islamic Azad University, P. O. Box 13185/768 Tehran, Iran
Version 1 : Received: 3 September 2016 / Approved: 5 September 2016 / Online: 5 September 2016 (09:58:58 CEST)

A peer-reviewed article of this Preprint also exists.

Rahimi, H.; Nabizadeh, K. Amenability Modulo an Ideal of Second Duals of Semigroup Algebras. Mathematics 2016, 4, 55. Rahimi, H.; Nabizadeh, K. Amenability Modulo an Ideal of Second Duals of Semigroup Algebras. Mathematics 2016, 4, 55.

Journal reference: Mathematics 2016, 4, 55
DOI: 10.3390/math4030055

Abstract

The aim of this paper is to investigate the amenability modulo an ideal of Banach algebras
with emphasis on applications to homological algebras. In doing so, we show that amenability modulo an ideal of A** implies amenability modulo an ideal of A. Finally, for a large class of semigroups, we prove that l1(S)** is amenable modulo Iσ** if and only if an appropriate group homomorphic image of S is finite where Iσ is the closed ideal induced by the least group congruence σ.

Subject Areas

amenability modulo an ideal; semigroup algebra; group congruence

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