, Volume 71, Issue 3, pp 471-480
Date: 03 Feb 2006

Paradoxical Decomposition of Semigroups

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Abstract

We introduce the concept of paradoxical decomposition for semigroups. We show that a semigroup S admits a left paradoxical decomposition if and only if S is not left amenable. Also Rosenbelatt and Willis introduced the configuration concept for groups and showed that amenability of groups is equivalent with existence of normalised solution for any system of configuration equations. We generalise it for semigroups.