Abstract
A ring R is called, according to [2], a left p.p. ring if any principal left ideal of R is projective. A ring which is left and right p.p. is called a p.p. ring.In this short note we shall give some additional remarks to A. Hattori [2]. In Proposition 1 we shall give a characterization of commutative p.p. rings, and in Proposition 3 we shall give a generalization of Proposition 17 and 18 in [2], which shows also that the modified torsion theory over commutative p.p. rings coincides with the usual torsion theory.
Publisher
Cambridge University Press (CUP)
Reference4 articles.
1. Endo S. , Regular rings and semi-hereditary rings, to appear.
2. A foundation of torsion theory for modules over general rings;Hattori;Nagoya Math. Jour.
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