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arXiv · 2610.36174

Finite Non-Commutative Centrally Essential Rings of Minimal Order

Adel Abyzov·Oleg Lyubimtsev·Askar Tuganbaev
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Abstract

A ring $R$ with non-zero identity element is said to be centrally essential if for any non-zero element $a$ of $R$, there exist non-zero central elements $x$ and $y$ such that $ax = y$. In the paper, we prove that the minimal order of a finite non-commutative centrally essential ring is equal to $64$. A partial classification of such rings is presented, and the existence of non-isomorphic non-commutative centrally essential rings of minimal order is proved.

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Adel Abyzov, Oleg Lyubimtsev, Askar Tuganbaev. 2026-10-26. Finite Non-Commutative Centrally Essential Rings of Minimal Order. https://arxiv.org/abs/2610.36174

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