Iranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16121220200601Approximate biprojectivity and biflatness of some algebras over certain semigroups14515510769810.30504/jims.2020.107698ENH.Pourmahmood-AghababaDepartment of Mathematics, University of Tabriz, Tabriz, Iran.M. H.SattariDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.Journal Article20190715We investigate (bounded) approximate biprojectivity of $l^1(S)$ for uniformly locally finite inverse semigroups. As a consequence, we show that when $S=\mathcal{M}(G, I)$ is the Brandt inverse semigroup, then $l^1(S)$ is (boundedly) approximately biprojective if and only if $G$ is amenable. Moreover, we study biflatness and (bounded) approximate biprojectivity of the measure algebra $M(S)$ of a topological Brandt semigroup.http://jims.ims.ir/article_107698_f1cce5a41ba06bdadbd87490a3330180.pdf