Some Characterizations for Approximate Biflatness of Semigroup Algebras

Abstract

In this paper, we study an approximate biflatness of l1S, where S is a Clifford semigroup. Indeed, we show that a Clifford semigroup algebra l1S is approximately biflat if and only if every maximal subgroup of S is amenable, ES is locally finite, and l1S has an approximate identity in c00S. Moreover, we prove that l1S is approximately biflat if and only if each maximal subgroup of S is amenable for an inverse semigroup S such that ES, the set of its idempotent elements, is totally ordered and locally finite.