零半群中的高交换子

IF 0.6 4区数学 Q3 MATHEMATICS

Algebra Universalis Pub Date : 2023-03-07 DOI:10.1007/s00012-023-00809-5

Jelena Radović, Nebojša Mudrinski

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引用次数: 0

摘要

我们引入了半群中理想的高级交换子的概念。对于具有零的半群，证明了里斯同余的高阶交换子等于相应理想的交换子的里斯同余。我们得到，对于Rees同余，高阶交换子是二元交换子的组成。因此，我们证明了在零的半群中，半群理论意义上的可解性、超幂零性、幂零性和幂零性的四个条件都是等价的。

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Higher commutators in semigroups with zero

We introduce the notion of the higher commutator of ideals in semigroups. For semigroups with zero, it is shown that the higher order commutator of Rees congruences is equal to the Rees congruence of the commutator of the corresponding ideals. We obtain that, for Rees congruences, higher order commutator is a composition of binary commutators. As a consequence, we prove that in semigroups with zero all four conditions of solvability, supernilpotency, nilpotency and nilpotency in the sense of semigroup theory, are equivalent.

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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.