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Mathematics 2016, 4(3), 55; doi:10.3390/math4030055

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, Tehran, Iran
*
Author to whom correspondence should be addressed.
Academic Editor: Hvedri Inassaridze
Received: 22 May 2016 / Revised: 27 August 2016 / Accepted: 2 September 2016 / Published: 13 September 2016
View Full-Text   |   Download PDF [245 KB, uploaded 13 September 2016]

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 l 1 ( S ) * * is amenable modulo I σ * * if and only if an appropriate group homomorphic image of S is finite, where I σ is the closed ideal induced by the least group congruence σ . View Full-Text
Keywords: amenability modulo an ideal; semigroup algebra; group congruence amenability modulo an ideal; semigroup algebra; group congruence
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. (CC BY 4.0).

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MDPI and ACS Style

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

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