Module (φ,ψ)-amenability of Banach Algebras
نویسندگان
چکیده
Let S be an inverse semigroup with the set of idempotents E and S/ ≈ be an appropriate group homomorphic image of S. In this paper we find a one-to-one correspondence between two cohomology groups of the group algebra `1(S) and the semigroup algebra `1(S/ ≈) with coefficients in the same space. As a consequence, we prove that S is amenable if and only if S/ ≈ is amenable. This could be considered as the same result of Duncan and Namioka [5] with another method which asserts that the inverse semigroup S is amenable if and only if the group homomorphic image S/ ∼ is amenable, where ∼ is a congruence relation on S.
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