For an inverse semigroup S with the set of idempotents E , we find necessary and sufficient conditions for the Fourier algebra A ( S ) to be module amenable, module character amenable, module (operator) biflat and module (operator) biprojective (as $$l^1(E)$$ l 1 ( E ) -module). Some examples show that when S is either a bicyclic inverse semigroup or a Brandt inverse semigroup, A ( S ) is module amenable, module biprojective and module biflat as well.

中文翻译：

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关于逆半群傅里叶代数的模上同调

对于具有一组幂等项 E 的逆半群 S，我们发现傅立叶代数 A ( S ) 是模适用的、模字符适用的、模（算子）双平坦和模（算子）双射的充分必要条件（如 $$ l^1(E)$$ l 1 ( E ) -模块)。一些例子表明，当 S 是双环逆半群或 Brandt 逆半群时，A ( S ) 是模服从的、模双射的和模双平的。