简化e喷泉半群的代数与广义样本恒等式2

Pub Date : 2023-11-08 DOI:10.1142/s0219498825500914
Itamar Stein
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引用次数: 0

摘要

本文研究了作者在前一篇文章中提出的广义右样本恒等式。设[公式:见文]是满足同余条件的约简[公式:见文]-喷泉半群。我们可以把[公式:见文]与一个小范畴[公式:见文]联系起来,它的对象集合与幂等的集合[公式:见文]一致,它的态射对应于[公式:见文]的元素。我们证明了[公式:见文]满足广义右样本恒等式当且仅当[公式:见文]的每一个元素在广义格林关系的某些类之间诱导出一个左[公式:见文]的同态。在这种情况下,我们将相关的范畴(公式:见文本)解释为半群代数的皮尔斯分解的离散形式。我们也给出了满足这个恒等式的半群的一些自然例子。
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Algebras of Reduced E-Fountain Semigroups and the Generalized Ample Identity II
We study the generalized right ample identity, introduced by the author in a previous paper. Let [Formula: see text] be a reduced [Formula: see text]-Fountain semigroup which satisfies the congruence condition. We can associate with [Formula: see text] a small category [Formula: see text] whose set of objects is identified with the set [Formula: see text] of idempotents and its morphisms correspond to elements of [Formula: see text]. We prove that [Formula: see text] satisfies the generalized right ample identity if and only if every element of [Formula: see text] induces a homomorphism of left [Formula: see text]-actions between certain classes of generalized Green’s relations. In this case, we interpret the associated category [Formula: see text] as a discrete form of a Peirce decomposition of the semigroup algebra. We also give some natural examples of semigroups satisfying this identity.
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