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Embedding torsionless modules in projectives.

Carl Faith (1990)

Publicacions Matemàtiques

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 Rn 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.

Embeddings of Kronecker modules into the category of prinjective modules and the endomorphism ring problem

Rüdiger Göbel, Daniel Simson (1998)

Colloquium Mathematicae

Endomorphism representations of Zorn rings and subclasses of rings with enough idempotents.

K.M. Rangaswamy (1975)

Journal für die reine und angewandte Mathematik

Errata-Corrige : “Linearly compact rings and strongly quasi-injective modules”

C. Menini (1983)

Rendiconti del Seminario Matematico della Università di Padova

Étude des sous-modules compléments dans un A-module

Guy Renault (1962/1963)

Séminaire Dubreil. Algèbre et théorie des nombres

Extending modules relative to a torsion theory

Semra Doğruöz (2008)

Czechoslovak Mathematical Journal

An $R$ -module $M$ is said to be an extending module if every closed submodule of $M$ is a direct summand. In this paper we introduce and investigate the concept of a type 2 $τ$ -extending module, where $τ$ is a hereditary torsion theory on $Mod$ - $R$ . An $R$ -module $M$ is called type 2 $τ$ -extending if every type 2 $τ$ -closed submodule of $M$ is a direct summand of $M$ . If $τ_{I}$ is the torsion theory on $Mod$ - $R$ corresponding to an idempotent ideal $I$ of $R$ and $M$ is a type 2 $τ_{I}$ -extending $R$ -module, then the question of whether or not $M / M I$ is...