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Displaying similar documents to “On Von Neumann regular rings, X.”

On p -injectivity, YJ-injectivity and quasi-Frobeniusean rings

Roger Yue Chi Ming (2002)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characterized in terms of special annihilators. Quasi-Frobeniusean rings are characterized in terms...

VNR rings, Π -regular rings and annihilators

Roger Yue Chi Ming (2009)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Von Neumann regular rings, hereditary rings, semi-simple Artinian rings, self-injective regular rings are characterized. Rings which are either strongly regular or semi-simple Artinian are considered. Annihilator ideals and Π -regular rings are studied. Properties of WGP-injectivity are developed.

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

Carl Faith (1992)

Publicacions Matemàtiques

Similarity:

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,...

Embedding torsionless modules in projectives.

Carl Faith (1990)

Publicacions Matemàtiques

Similarity:

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.