When every flat ideal is projective

Fatima Cheniour; Najib Mahdou

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Displaying similar documents to “When every flat ideal is projective”

Rings with zero intersection property on annihilators: Zip rings.

Carl Faith (1989)

Publicacions Matemàtiques

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Zelmanowitz [12] introduced the concept of ring, which we call right zip rings, with the defining properties below, which are equivalent: (ZIP 1) If the right anihilator X^⊥ of a subset X of R is zero, then X₁ ^⊥ = 0 for a finite subset X₁ ⊆ X. (ZIP 2) If L is a left ideal and if L^⊥ = 0, then L₁ ...

On quasi-Frobeniusean and Artinian rings.

Yue Chi Ming, Roger (1983)

Publications de l'Institut Mathématique. Nouvelle Série

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On some properties of polynomial rings.

Al-Ezeh, H. (1987)

International Journal of Mathematics and Mathematical Sciences

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On injectivity, p-injectivity and YJ-injectivity.

Yue Chi Ming, R. (2004)

Acta Mathematica Universitatis Comenianae. New Series

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Non-commutative Dedekind rings

A. W. Goldie (1967-1968)

Séminaire Dubreil. Algèbre et théorie des nombres

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Polynomial rings over Jacobson-Hilbert rings.

Carl Faith (1989)

Publicacions Matemàtiques

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A ring R is (in Vámos' terminology) if every subdirectly irreducible factor ring R/I is self-injective. rings include Noetherian rings, Morita rings and almost maximal valuation rings ([V1]). In [F3] we raised the question of whether a polynomial ring R[x] over a ring R is again . In this paper we show this is not the case.

Self-injective Von Neumann regular subrings and a theorem of Pere Menal.

Carl Faith (1992)

Publicacions Matemàtiques

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This paper owes its origins to Pere Menal and his work on Von Neumann Regular (= VNR) rings, especially his work listed in the bibliography on when the tensor product K = A ⊗ B of two algebras over a field k are right self-injective (= SI) or VNR. Pere showed that then A and B both enjoy the same property, SI or VNR, and furthermore that either A and B are algebraic algebras over k (see [M]). This is connected with a lemma in the proof of the , namely a finite ring extension K = k[a,...

Commutative rings in which every proper ideal is maximal

Joachim Reineke (1977)

Fundamenta Mathematicae

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Embedding torsionless modules in projectives.

Carl Faith (1990)

Publicacions Matemàtiques

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In this paper we study a condition right FGTF on a ring R, namely when all finitely generated torsionless right R-modules embed in a free module. We show that for a von Neuman regular (VNR) ring R the condition is equivalent to every matrix ring R is a Baer ring; and this is right-left symmetric. Furthermore, for any Utumi VNR, this can be strengthened: R is FGTF iff R is self-injective.

A property of A-sequences

R. Hartshorne (1966)

Bulletin de la Société Mathématique de France

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