Semigroup Forum, ( ISI ), Volume (92), No (1), Year (2016-1) , Pages (304-310)

Title : ( Arens regularity of certain weighted semigroup algebras and countability )

Authors: Hamid Reza Ebrahimi Vishki , Bahram Khodsiani , Ali Rejali ,
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Abstract

In this paper, among other things, we show that for a large class of semi-groups, the Arens regularity of the weighted semigroup algebra ℓ1(S,w) implies the countability of S. This generalizes the main results of Craw and Young [Quart. J. Math.25 (1974), 351-358], stating that every countable semigroup admits a weight w for which ℓ1(S,w) is Arens regular and no uncountable group admits such a weight.

Keywords

Arens regularity; weighted semigroup algebra; completely simple semigroup; inverse semigroup.