论文标题
减少$ e $ fountain semigroups和广义丰富身份II的代数II
Algebras of reduced $E$-Fountain semigroups and the generalized ample identity II
论文作者
论文摘要
我们研究了作者在上一篇论文中介绍的广义右透明身份。让$ s $是减少$ e $ fount-fountain semigroup，满足一致性条件。我们可以与$ s $ A小型类别$ \ MATHCAL {C}（S）$相关联，其对象集与IDEMPOTENTS的集合$ e $一起识别，其形态及其形态对应于$ s $的元素。我们证明，$ s $仅当$ s $的每个元素引起某些类别的广义格林关系之间的左$ s $ actions的同构时，才能满足广义的充分身份。在这种情况下，我们将关联的类别$ \ MATHCAL {C}（s）$解释为Semogroup代数的Peirce分解的一种离散形式。我们还给出了一些满足这种身份的半群的自然例子。
We study the generalized right ample identity, introduced by the author in a previous paper. Let $S$ be a reduced $E$-Fountain semigroup which satisfies the congruence condition. We can associate with $S$ a small category $\mathcal{C}(S)$ whose set of objects is identified with the set $E$ of idempotents and its morphisms correspond to elements of $S$. We prove that $S$ satisfies the generalized right ample identity if and only if every element of $S$ induces a homomorphism of left $S$-actions between certain classes of generalized Green's relations. In this case, we interpret the associated category $\mathcal{C}(S)$ as a discrete form of a Peirce decomposition of the semigroup algebra. We also give some natural examples of semigroups satisfying this identity.
