Principally Quasi-Baer Skew Power Series Rings

Abstract

Let α be an endomorphism of R which is not assumed to be surjective and R be α-compatible. It is shown that the skew power series ring R[[x; α]] is right p.q.-Baer if and only if the skew Laurent series ring R[[x, x ⁻¹; α]] is right p.q.-Baer if and only if R is right p.q.-Baer and every countable subset of right semicentral idempotents has a generalized countable join. Examples to illustrate and delimit the theory are provided.

Key Words:

• Annihilators
• Baer rings
• Quasi-Baer rings
• Right p.q.-Baer rings
• Semicentral idempotents
• Skew Laurent series rings
• Skew power series rings

2000 Mathematics Subject Classification:

• Primary 16S36, 16E50
• Secondary 16W60