Module amenability and module biprojectivity of θ-Lau product of Banach algebras

Subject Areas : Group theory

D. Ebrahimi Bagha ¹ , H. Azaraien ²

1 - Department of Mathematics, Islamic Azad university, Central Tehran Branch, Tehran, Iran
2 - Department of Mathematics, Islamic Azad university, Central Tehran Branch, Tehran, Iran

Received: 2014-10-02 Accepted : 2015-12-29 Published : 2014-12-30

Keywords: Module amenability, module biprojectivity, inverse semigroup, θ-Lau product of Banach algebras,

Abstract :

In this paper we study the relation between module amenability of $\theta$-Lau product $A×_\theta B$ and that of Banach algebras $A, B$. We also discuss module biprojectivity of $A×\theta B$. As a consequent we will see that for an inverse semigroup $S$, $l^1(S)×_\theta l^1(S)$ is module amenable if and only if $S$ is amenable.

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