Communications of the Korean Mathematical Society (대한수학회논문집)

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MODULE AMENABILITY AND MODULE ARENS REGULARITY OF WEIGHTED SEMIGROUP ALGEBRAS

  • Received : 2017.07.30
  • Accepted : 2019.05.02
  • Published : 2019.07.31
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Abstract

For every inverse semigroup S with subsemigroup E of idempotents, necessary and sufficient conditions are obtained for the weighted semigroup algebra $l^1(S,{\omega})$ and its second dual to be $l^1(E)$-module amenble. Some results for the module Arens regularity of $l^1(S,{\omega})$ (as an $l^1(E)$-module) are found. If S is either of the bicyclic inverse semigroup or the Brandt inverse semigroup, it is shown that $l^1(S,{\omega})$ is module amenable but not amenable for any weight ${\omega}$.

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References

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