[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2022.62.2.213

The Relation Between Units and Nilpotents

Cheon, Jeoung Soo (Department of Mathematics, Pusan National University)
Kwak, Tai Keun (Department of Data Science, Daejin University)
Lee, Yang (Department of Mathematics, Yanbian University, Institute for Applied Mathematics and Optics, Hanbat National University)
Seo, Young Joo (Department of Data Science, Daejin University)

Publication Information

Kyungpook Mathematical Journal / v.62, no.2, 2022 , pp. 213-227 More about this Journal

Abstract

We discuss the relation between units and nilpotents of a ring, concentrating on the transitivity of units on nilpotents under regular group actions. We first prove that for a ring R, if U(R) is right transitive on N(R), then Köthe's conjecture holds for R, where U(R) and N(R) are the group of all units and the set of all nilpotents in R, respectively. A ring is called right UN-transitive if it satisfies this transitivity, as a generalization, a ring is called unilpotent-IFP if aU(R) ⊆ N(R) for all a ∈ N(R). We study the structures of right UN-transitive and unilpotent-IFP rings in relation to radicals, NI rings, unit-IFP rings, matrix rings and polynomial rings.

Keywords

transitivity of units; right UN-transitive ring; unilpotent-IFP ring; unit; nilpotent; nilradical; NI ring;

Citations & Related Records

Times Cited By KSCI : 2 (Citation Analysis)

Reference
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