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On right duo p.p. rings. (English) Zbl 0709.16007

A ring is called a right duo ring if every right ideal is twosided. It is proved that for a right duo ring the following statements are equivalent: (1) The ring is right semihereditary. (2) Every ideal generated by two elements is right projective. (3) Principal ideals are right projective and the weak global dimension is at most one.
The result is proved by showing that a duo p.p. ring has a von Neumann regular quotient ring and then applying recent results of A. A. Tuganbaev.
It is well known that (1)-(3) are equivalent for commutative rings.
The authors also show that in a right duo p.p. ring finitely generated right projective ideals are left projective and direct summands of invertible ideals.
Reviewer: S.Jøndrup

MSC:

16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.
16D25 Ideals in associative algebras
16E10 Homological dimension in associative algebras
16S90 Torsion theories; radicals on module categories (associative algebraic aspects)
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References:

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