Iranian Mathematical Society Journal of the Iranian Mathematical Society 2717-1612 1 2 2020 12 01 Approximate biprojectivity and biflatness of some algebras over certain semigroups 145 155 107698 10.30504/jims.2020.107698 EN H. Pourmahmood-Aghababa Department of Mathematics‎, University of ‎Tabriz‎, ‎Tabriz‎, ‎Iran. M. H. Sattari Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran. Journal Article 2019 07 15 ‎We 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. https://jims.ims.ir/article_107698_6045e6aa7bdd0a3874cf02e1f510e615.pdf