We utilize the notion of module extension to reduce the problem of stability of derivations to that of ring homomorphisms studied by R. Badora in the context of Banach bimodules over Banach algebras. AMS subject classifications: Primary 39B82; Secondary 39B52, 46H25

In this corrigendum, we give a correction of one result in reference [1].

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 consider...

Assume that $A$‎, ‎$B$ are Banach algebras and that $m:Atimes Brightarrow B$‎, ‎$m^prime:Atimes Arightarrow B$ are bounded bilinear mappings‎. ‎We study the relationships between Arens regularity of $m$‎, ‎$m^prime$ and the Banach algebras $A$‎, ‎$B$‎. ‎For a Banach $A‎$‎-bimodule $B$‎, ‎we show that $B$ factors with respect to $A$ if and only if $B^{**}$ is unital as an $A^{**}‎$‎-module‎. ‎Le...