Some Characterizations for Approximate Biflatness of Semigroup Algebras

Abstract

In this paper, we study an approximate biflatness of$l^1\left(S\right)$, where$S$is a Clifford semigroup. Indeed, we show that a Clifford semigroup algebra$l^1\left(S\right)$is approximately biflat if and only if every maximal subgroup of$S$is amenable,$E\left(S\right)$is locally finite, and$l^1\left(S\right)$has an approximate identity in$c_{00}\left(S\right)$. Moreover, we prove that$l^1\left(S\right)$is approximately biflat if and only if each maximal subgroup of$S$is amenable for an inverse semigroup$S$such that$E\left(S\right)$, the set of its idempotent elements, is totally ordered and locally finite.