arXiv subjects

Nebojša Mudrinski

Publications and source records attributed to Nebojša Mudrinski.

7 recordsLinked to original sources

arXiv2026

(Super)nilpotency and solvability in algebras with zero

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.

math.RA↗

arXiv2025

Supernilpotent Semirings

We prove that supernilpotent and nilpotent semirings with absorbing zero are the same and provide a necessary and sufficient condition for supernilpotency (nilpotency).

math.RA↗

arXiv2023

Commutators in Completely Simple Semigroups

We obtain a characterization of the binary commutator on completely simple semigroups, using their Rees matrix representation. Consequently, we prove that a regular semigroup is nilpotent (solvable) if and only if it is simple, and all its $\mathcal{H}$-classes are nilpotent (solvable) groups.

math.RA↗

arXiv2023

Supernilpotent Semigroups

Regular abelian semigroups are isomorphic to a direct product of an abelian group and a rectangular band (Warne, 1994). Seeking for a similar result for nilpotency, solvability and supernilpotency of regular semigroups, we obtain that analogous statement is true only in orthodox semigroups. We provide an example that shows that the same does not have to be true in regular semigroups that are not orthodox.

math.GR↗

arXiv2022

Finite representation of commutator sequences

Several structural properties of a universal algebra can be seen from the higher commutators of its congruences. Even on a finite algebra, the sequence of higher commutator operations is an infinite object. In the present paper, we exhibit finite representations of this sequence.

math.RA↗

arXiv2017

Complexity of term representations of finitary functions

The clone of term operations of an algebraic structure consists of all operations that can be expressed by a term in the language of the structure. We consider bounds for the length and the height of the terms expressing these functions, and we show that these bounds are often robust against the change of the basic operations of the structure.

math.RA↗

arXiv2015

Finite generation of congruence preserving functions

We investigate when the clone of congruence preserving functions is finitely generated. We obtain a full description for all finite $p$-groups, and for all finite algebras with Mal'cev term and simple congruence lattice. The characterization for $p$-groups allows a generalization to a large class of expansions of groups.

math.RA↗