First and Second Module Cohomology Groups for Non Commutative Semigroup Algebras

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‎Let $S$ be a (not necessarily commutative) Clifford semigroup with idempotent set $E$. In this paper, we show that the first (second) Hochschild cohomology group and the first (second) module cohomology group of semigroup algbera $ell^1(S)$ with coefficients in $ell^infty(S)$ (and also $ell^1(S)^{(2n-1)}$ for $nin mathbb{N}$) are equal.