STRUCTURE OF UNIT-IFP RINGS

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...

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Bibliographic Details
Published inJournal of the Korean Mathematical Society Vol. 55; no. 5; pp. 1257 - 1268
Main Author Lee, Yang
Format Journal Article
LanguageKorean
Published 2018
Subjects
unit
descending chain condition for nil left ideals
nilradical
K{\ddot{o}}the^{\prime}s$ conjecture
group action of units on nilpotent elements
orbit
nilpotent element
unit-IFP ring
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Summary: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.
Bibliography:KISTI1.1003/JNL.JAKO201828138443702
ISSN:0304-9914