Quasi-Baer ring extensions and biregrular rings

By G. Birkenmeier, Jin Yong Kim, J. Park. Bulletin of the Australian Mathematical Society, 2000

54 citations recorded by the source corpus.

A ring R with unity is called a (quasi-) Baer ring if the left annihilator of every (left ideal) nonempty subset of R is generated (as a left ideal) by an idempotent. Armendariz has shown that if R is a reduced PI-ring whose centre is Baer, then R is Baer. We generalise his result by considering the broader question: when does the (quasi-) Baer condition extend to a ring from a subring? Also it is well known that a regular ring is Baer if and only if its lattice of principal right ideals is complete. Analogously, we prove that a biregular ring is quasi-Baer if and only if its lattice of principal ideals is complete.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/29aaac2da9f2e417c59197e06325b5bb08ef1c30

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In Algebra and Number Theory

1. S. Tariq Rizvi
2. C. Roman
3. Gangyong Lee
4. G. Birkenmeier

In Computational Theory and Mathematics

1. S. Tariq Rizvi
2. C. Roman
3. G. Birkenmeier

Citations in the corpus

• Baer and Quasi-Baer Modules (2004, background): “Several types of polynomial extensions of quasi-Baer rings are quasi-Baer (see, for example, Theorem 2.4, Birkenmeier et al., 2000d).”
• Modules in Which Every Fully Invariant Submodule is Essential in a Direct Summand (2002, background): “Hence the equivalence, (i),(ii), follows from ([19], Proposition 1.”
• Dual Rickart Modules (2011, background): “The following example due to Birkenmeier, Kim, and Park [ 3 , Example 1.”