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arXiv · 2610.03348

(Super)nilpotency and solvability in algebras with zero

Ivana Đurđev·Nebojša Mudrinski
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Abstract

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.

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Ivana Đurđev, Nebojša Mudrinski. 2026-10-02. (Super)nilpotency and solvability in algebras with zero. https://arxiv.org/abs/2610.03348

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