In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup...In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup S, the notions of amenability, approximate amenability and bounded approximate amenability of e1（S） are equivalent. We use this to give a direct proof of the approximate amenability of e1 （S） for a Brandt semigroup S. Moreover, we characterize the approximate amenability of e1（S）, where S is a uniformly locally finite band semigroup.展开更多
文摘In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup S, the notions of amenability, approximate amenability and bounded approximate amenability of e1（S） are equivalent. We use this to give a direct proof of the approximate amenability of e1 （S） for a Brandt semigroup S. Moreover, we characterize the approximate amenability of e1（S）, where S is a uniformly locally finite band semigroup.
