Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Đurđev, Ivana, Mudrinski, Nebojša
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220452061