Displaying similar documents to “Rings with zero intersection property on annihilators: Zip rings.”

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.

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.

When every flat ideal is projective

Fatima Cheniour, Najib Mahdou (2014)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we study the class of rings in which every flat ideal is projective. We investigate the stability of this property under homomorphic image, and its transfer to various contexts of constructions such as direct products, and trivial ring extensions. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.

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,...