Polynomial extensions of Baer and quasi-Baer rings

By G. Birkenmeier, Jin Yong Kim, J. Park. 2001

165 citations recorded by the source corpus.

Abstract A ring R is called (quasi-) Baer if the right annihilator of every (ideal) nonempty subset of R is generated, as a right ideal, by an idempotent of R . Armendariz has shown that for a reduced ring R (i.e., R has no nonzero nilpotent elements), R is Baer if and only if R [ x ] is Baer. In this paper, we show that for many polynomial extensions (including formal power series, Laurent polynomials, and Laurent series), a ring R is quasi-Baer if and only if the polynomial extension over R is quasi-Baer. As a consequence, we obtain a generalization of Armendariz's result for several types of polynomial extensions over reduced rings.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/61a252ceedaa5a4e0e18fd995418b1b80a141d66

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In Algebra and Number Theory

In Computational Theory and Mathematics

Citations in the corpus

Power Series Rings Satisfying a Zero Divisor Property (2006, background): “…noncommutative reduced rings in the statements before Anderson and Camillo (1998, Example 10); while Birkenmeier et al. observed the (quasi-)Baerness of polynomial rings and power series rings, generalizing Armendariz’s result for several types of polynomial extensions (Birkenmeier et al., 2001).”
On direct sums of Baer modules (2009, background): “A number of research papers have been published on Baer and quasi-Baer rings, see for example [1], [2], [3], [4], [5], [6], [26].”