Work

Completely centrally essential rings

Year: 2025

Type: article

Abstract: A ring R is said to be centrally essential if for every its nonzero element a, there exist nonzero central elements x and y with [Formula: see text]. A ring R is said to be completely centrally essential if all its factor rings are centrally essential rings. It is proved that completely centrally essential semiprimary rings are Lie nilpotent; noetherian completely centrally essential rings are strongly Lie nilpotent (in particular, every such ring is a [Formula: see text]-ring). Every completely centrally essential ring has the classical ring of fractions which is a completely centrally essential ring. If R is a commutative domain and G is an arbitrary group, then any completely centrally essential group ring [Formula: see text] is commutative.

Source: International Journal of Algebra and Computation

DOI: 10.1142/s0218196725500274

Authors: Oleg Lyubimtsev, Askar Tuganbaev

Institutions: Moscow Power Engineering Institute, Lomonosov Moscow State University

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Ministry of Education and Science of the Russian Federation, Russian Science Foundation

Awards: G5219570974, G8185072082