[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j170676

STRUCTURE OF UNIT-IFP RINGS

Lee, Yang (Institute of Basic Science Daejin University)

Publication Information

Journal of the Korean Mathematical Society / v.55, no.5, 2018 , pp. 1257-1268 More about this Journal

Abstract

In this article we first investigate a sort of unit-IFP ring by which Antoine provides very useful information to ring theory in relation with the structure of coefficients of zero-dividing polynomials. Here we are concerned with the whole shape of units and nilpotent elements in such rings. Next we study the properties of unit-IFP rings through group actions of units on nonzero nilpotent elements. We prove that if R is a unit-IFP ring such that there are finite number of orbits under the left (resp., right) action of units on nonzero nilpotent elements, then R satisfies the descending chain condition for nil left (resp., right) ideals of R and the upper nilradical of R is nilpotent.

Keywords

unit-IFP ring; unit; nilpotent element; group action of units on nilpotent elements; descending chain condition for nil left ideals; orbit; nilradical; $K{\ddot{o}}the^{\prime}s$ conjecture;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

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