并非所有零势单元都是有限相关的

IF 0.6 4区数学 Q3 MATHEMATICS

Algebra Universalis Pub Date : 2024-02-14 DOI:10.1007/s00012-023-00841-5

Markus Steindl

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引用次数: 0

摘要

如果一个有限半群的项函数是由一组有限的有限关系决定的，那么这个有限半群就是有限相关的（具有有限度）。例如，众所周知，所有零势半群都是有限相关的。零potent monoid 是具有邻接同一性的零potent 半群。我们证明了每个 4-nilpotent monoid 都是有限相关的。我们还给出了一个不有限相关的 5-nilpotent monoid 的例子。据我们所知，这是第一个有限相关半群的例子，在这个半群中，与一个标识相邻会产生一个非有限相关的半群。我们还提供了有限相关半群的例子，这些半群有非有限相关的子半群、同态图像，特别是里斯商。

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Not all nilpotent monoids are finitely related

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.

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来源期刊

Algebra Universalis 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3 months

期刊介绍： Algebra Universalis publishes papers in universal algebra, lattice theory, and related fields. In a pragmatic way, one could define the areas of interest of the journal as the union of the areas of interest of the members of the Editorial Board. In addition to research papers, we are also interested in publishing high quality survey articles.