First and Second Module Cohomology Groups for Non Commutative Semigroup Algebras

Let S be a (not necessarily commutative) Clifford semi group with idempotent set E. In this paper, we show that the first (second) Hochschild cohomology group and the first (second) mod ule cohomology group of semigroup algbera ℓ 1 (S) with coefficients in ℓ ∞(S) (and also ℓ 1 (S) (2n−1) for n ∈ N) are equal.