A ring R is called, according to , 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 . 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 , which shows also that the modified torsion theory over commutative p.p. rings coincides with the usual torsion theory.
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