Document Type: Research Paper


Faculty of Mathematics Science and Statistics, University of Birjand, Birjand, 9717851367, Iran.


‎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 $n\in \mathbb{N}$) are equal.


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