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Amenability Modulo an Ideal of Second Duals of Semigroup Algebras
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.
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.
Keywords
amenability modulo an ideal; semigroup algebra; group congruence
Subject
MATHEMATICS & COMPUTER SCIENCE, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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