Module derivations on inverse semigroup algebras
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/حکیمه محمدی
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: علوم ریاضی
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چاپی - الکترونیکی
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s, t S, e E. This dissertation is based on the following papers: 1. Davood Ebrahimi Bagha and Massoud Amini, Module derivation problem for inverse semigroups, Semigroup Forum, 85 (2012), 525-532. 2. Davood Ebrahimi Bagha and Massoud Amini, Module derivations on semigroup algebras, Semigroup Forum, 94 (2017), 176-180|The derivation problem for a locally compact group G asserts that each bounded derivation from L1(G) to L1(G) is implemented by an element of M(G). Recently a simple proof of this result was announced. We show that basically the same argument with some extra manipulations with idempotents solves the module derivation problem for inverse semigroups, asserting that for an inverse semigroup S with set of idempotents E and maximal group homomorphic image GS, if E acts on S trivially from the left and by mutiplication from the right, any bounded module derivation from l1(S) to l1(GS) is inner. Then we show that every bounded module derivation from l1(S) to (l1(S)/J) = J? is inner, where J is the closed ideal of l1(S) generated by the set set st
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Module derivations on inverse semigroup algebras