On PP-rings

descriptionPublicationkeyboard_double_arrow_right Article 01 Oct 1993 English Publisher:Springer Science and Business Media LLCJournal:Periodica Mathematica Hungarica, volume 27, pages 85-88 (issn: 0031-5303, eissn: 1588-2829,

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Authors: Nicholson, W. K.;

doi: 10.1007/bf01876633

On PP-rings

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Abstract

A ring \(R\) is called a left PP-ring if every principal left ideal is projective. The author gives a new characterization of left PP-rings, uses that to give an elementary proof of a result of the reviewer [Kobe J. Math. 7, No. 1, 77-80 (1990; Zbl 0726.16003)] characterizing triangular PP-rings, and then determines when the ring \(T_ n(R)\) of upper triangular matrices over \(R\) is a left PP-ring.

Related Organizations

University of Calgary
Canada

Keywords

left PP-rings, Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc., principal left ideal, Free, projective, and flat modules and ideals in associative algebras, von Neumann regular rings and generalizations (associative algebraic aspects), triangular PP-rings, upper triangular matrices, Endomorphism rings; matrix rings, Ideals in associative algebras

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