On Skew Power Serieswise Armendariz Rings

Abstract

For a ring endomorphism α, we introduce and investigate SPA-rings which are a generalization of α-rigid rings and determine the radicals of the skew polynomial rings R[x; α], R[x, x ⁻¹; α] and the skew power series rings R[[x; α]], R[[x, x ⁻¹; α]], in terms of those of R. We prove that several properties transfer between R and the extensions, in case R is an SPA-ring. We will construct various types of nonreduced SPA-rings and show SPA is a strictly stronger condition than α-rigid.

Key Words:

• Armendariz ring
• Baer ring
• Jacobson radical
• Skew polynomial ring
• Skew power series ring

2000 Mathematics Subject Classification:

• 16W60
• 16S36

ACKNOWLEDGMENT

The authors are thankful to the referee for a careful reading of the article and for some helpful comments and suggestions.

Notes

Communicated by V. A. Artamonov.