发表机构
University of Novi Sad（诺维萨德大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对含零代数引入理想的高阶交换子与Rees同余，证明二者交换子对应关系，并据此刻画n-超幂零性、n-幂零性及含零广群中的n-可解性。
AI 中文摘要
含零代数是指包含一个称为零的元素0的代数，使得所有基本运算都具有如下性质：只要至少一个自变量取值为0，运算结果即为0。我们为这类代数引入了理想的高阶交换子与Rees同余的概念。证明了Rees同余的交换子等于相应理想的交换子所对应的Rees同余。我们应用这一结果给出了含零代数中n-超幂零性和n-幂零性的刻画，以及含零广群中n-可解性的刻画。
英文摘要
An algebra with zero is an algebra that contains an element 0, called zero, such that all fundamental operations have the property that the result is zero whenever at least one of the arguments takes the value 0. We introduce the notion of the higher commutator of ideals and Rees congruences for such algebras. It is shown that the commutator of Rees congruences is equal to the Rees congruence of the commutator of the corresponding ideals. We apply this result to provide characterisations of n-supernilpotency and n-nilpotency in algebras with zero, as well as n-solvability in groupoids with zero.
Comments21 pages, 1 figure, 1 table
