论文标题
并非所有的nilpotent himoid均有限相关
Not all nilpotent monoids are finitely related
论文作者
论文摘要
如果有限的术语函数由有限的限制关系确定，则有限的半群有限相关（具有有限程度）。例如，众所周知，所有nilpotent的半群都是有限关联的。 nilpotent单体是具有相邻身份的nilpotent半群。我们表明，每$ 4 $ nilpotent monoid有限相关。我们还举例说明了$ 5 $ nilpotent monoid，这无限相关。据我们所知，这是有限相关的半群的第一个例子，其中相邻的身份产生了无限相关的半群。我们还提供了有限相关的半群的示例，这些半群具有非有限相关的子群，同构图像，尤其是REES商。
A finite semigroup is finitely related (has finite degree) if its term functions are determined by a finite set of finitary relations. For example, it is known that all nilpotent semigroups are finitely related. A nilpotent monoid is a nilpotent semigroup with adjoined identity. We show that every $4$-nilpotent monoid is finitely related. We also give an example of a $5$-nilpotent monoid that is not finitely related. To our knowledge, this is the first example of a finitely related semigroup where adjoining an identity yields a semigroup which is not finitely related. We also provide examples of finitely related semigroups which have subsemigroups, homomorphic images, and in particular Rees quotients, that are not finitely related.
