NILRADICALS OF SKEW POWER SERIES RINGS

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 41, Issue 3, 2004, pp.507-519
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2004.41.3.507

Title & Authors

NILRADICALS OF SKEW POWER SERIES RINGS

Hong, Chan-Yong; Kim, Nam-Kyun; Kwak, Tai-Keun;

Hong, Chan-Yong; Kim, Nam-Kyun; Kwak, Tai-Keun;

Abstract

For a ring endomorphism of a ring R, J. Krempa called a rigid endomorphism if a(a)＝0 implies a＝0 for a R. A ring R is called rigid if there exists a rigid endomorphism of R. In this paper, we extend the (J`-rigid property of a ring R to the upper nilradical (R) of R. For an endomorphism R and the upper nilradical (R) of a ring R, we introduce the condition (*): (R) is a -ideal of R and a(a) (R) implies a (R) for a R. We study characterizations of a ring R with an endomorphism satisfying the condition (*), and we investigate their related properties. The connections between the upper nilradical of R and the upper nilradical of the skew power series ring R[[;]] of R are also investigated.ated.

Keywords

rigid endomorphisms;the upper nilradicals;skew power series rings;

Language

English

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