对合匹配、保向和反向映射半群及全变换半群的逆覆盖
Involution matchings, the semigroup of orientation-preserving and orientation-reversing mappings, and inverse covers of the full transformation semigroup
摘要：
我们继续研究置换的有限正则半群，每个元素映射到它的逆之一，提供了一个完整的描述的情况下，半群的幂等元生成的子半群是一个联盟的群体。我们展示了，在两种方式，如何构建一个对合匹配的半群上的所有变换，无论是保持或反转方向的有限周期。最后，作为应用，证明了有限全变换半群不被交闭的逆半群覆盖。
英文摘要：
We continue the study of permutations of a finite regular semigroup that map each element to one of its inverses, providing a complete description in the case of semigroups whose idempotent generated subsemigroup is a union of groups. We show, in two ways, how to construct an involution matching on the semigroup of all transformations which either preserve or reverse orientation of a finite cycle. Finally, by way of application, we prove that finite full transformation semigroups have no cover by inverse semigroups that is closed under intersection.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
