2025/03/25 by O. V. Lyubimtsev, Lyubimtsev, Oleg, A. A. Tuganbaev +1
Mathematics · #Rings, Modules, and Algebras #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2503.20009
A ring R is said to be centrally essential if for every its non-zero element a, there exist non-zero central elements x and y with ax = y. 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 a ring is a PI-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 RG is commutative.