On PP-rings |
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Authors: | W. K. Nicholson |
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Affiliation: | (1) Department of Mathematics and Statistics, The University of Calgary, 2500 University Drive N.W., T2N 1N4 Calgary, Alberta, Canada |
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Abstract: | A ringR is called a leftPP-ring if every principal left ideal is projective, equivalently if the left annihilatorl(a) is generated by an idempotent for allaR. These rings seem first to have been discussed by Hattori [2] and examples include (von Neumann) regular rings and domains (possibly noncommutative). In this note we give a new characterization of leftPP-rings, use that to give an elementary proof of a result of Xue [4] characterizing triangularPP-rings, and then determine when the ringTn(R) of upper triangular matrices overR is a leftPP-ring. Throughout the paper all rings have a unity and all modules are unitary.This research was supported by NSERC Grant A8075 |
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Keywords: | Primary 16E60 |
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