Geodesic
Module $(\varphi,\psi)$-amenability of Banach algebras
Archivum mathematicum, Tome 46 (2010) no. 4, pp. 227-235 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $S$ be an inverse semigroup with the set of idempotents $E$ and $S/\approx$ 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 $\ell ^1(S)$ and the semigroup algebra $ {\ell ^{1}}(S/\approx )$ with coefficients in the same space. As a consequence, we prove that $S$ is amenable if and only if $S/\approx $ 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/\sim $ is amenable, where $\sim $ is a congruence relation on $S$.
Let $S$ be an inverse semigroup with the set of idempotents $E$ and $S/\approx$ 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 $\ell ^1(S)$ and the semigroup algebra $ {\ell ^{1}}(S/\approx )$ with coefficients in the same space. As a consequence, we prove that $S$ is amenable if and only if $S/\approx $ 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/\sim $ is amenable, where $\sim $ is a congruence relation on $S$.
Classification : 43A07, 46H25
Keywords: Banach modules; module derivation; module amenability; inverse semigroup 
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     author = {Bodaghi, Abasalt},
     title = {Module $(\varphi,\psi)$-amenability of {Banach} algebras},
     journal = {Archivum mathematicum},
     pages = {227--235},
     year = {2010},
     volume = {46},
     number = {4},
     mrnumber = {2754062},
     zbl = {1240.43001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2010_46_4_a0/}
}
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Bodaghi, Abasalt. Module $(\varphi,\psi)$-amenability of Banach algebras. Archivum mathematicum, Tome 46 (2010) no. 4, pp. 227-235. http://geodesic.mathdoc.fr/item/ARM_2010_46_4_a0/

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