Rings Which Are Essential over Their Centers
Victor Markov, Askar Tuganbaev
TL;DR
This paper explores the properties and examples of centrally essential rings, which are rings that are essential extensions of their centers, contributing to the understanding of their structure in noncommutative algebra.
Contribution
It provides new examples and describes properties of noncommutative centrally essential rings, advancing the theoretical understanding of these algebraic structures.
Findings
Several examples of noncommutative centrally essential rings
Properties of centrally essential rings described
Insights into the structure of rings as modules over their centers
Abstract
A centrally essential ring is a ring which is an essential extension of its center (we consider the ring as a module over its center). We give several examples of noncommutative centrally essential rings and describe some properties of centrally essential rings. V.T.Markov is supported by the Russian Foundation for Basic Research, project 17-01-00895-A. A.A.Tuganbaev is supported by Russian Scientific Foundation, project 16-11-10013.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Algebraic structures and combinatorial models