NILRADICALS OF SKEW POWER SERIES RINGS

Title & Authors
NILRADICALS OF SKEW POWER SERIES RINGS
Hong, Chan-Yong; Kim, Nam-Kyun; Kwak, Tai-Keun;

Abstract
For a ring endomorphism $\small{\sigma}$ of a ring R, J. Krempa called $\small{\sigma}$ a rigid endomorphism if a$\small{\sigma}$(a)＝0 implies a＝0 for a $\small{{\in}}$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 $\small{N_{r}}$(R) of R. For an endomorphism R and the upper nilradical $\small{N_{r}}$(R) of a ring R, we introduce the condition (*): $\small{N_{r}}$(R) is a $\small{\sigma}$-ideal of R and a$\small{\sigma}$(a) $\small{{\in}}$ $\small{N_{r}}$(R) implies a $\small{{\in}}$ $\small{N_{r}}$(R) for a $\small{{\in}}$ R. We study characterizations of a ring R with an endomorphism $\small{\sigma}$ 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[[$\small{\chi}$;$\small{\sigma}$]] of R are also investigated.ated.
Keywords
rigid endomorphisms;the upper nilradicals;skew power series rings;
Language
English
Cited by
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