Displaying similar documents to “Quasi-Frobenius quotient rings.”

There is no analog of the transpose map for infinite matrices.

Juan Jacobo Simón (1997)

Publicacions Matemàtiques

Similarity:

In this note we show that there are no ring anti-isomorphism between row finite matrix rings. As a consequence we show that row finite and column finite matrix rings cannot be either isomorphic or Morita equivalent rings. We also show that antiisomorphisms between endomorphism rings of infinitely generated projective modules may exist.

A criterion for rings which are locally valuation rings

Kamran Divaani-Aazar, Mohammad Ali Esmkhani, Massoud Tousi (2009)

Colloquium Mathematicae

Similarity:

Using the notion of cyclically pure injective modules, a characterization of rings which are locally valuation rings is established. As applications, new characterizations of Prüfer domains and pure semisimple rings are provided. Namely, we show that a domain R is Prüfer if and only if two of the three classes of pure injective, cyclically pure injective and RD-injective modules are equal. Also, we prove that a commutative ring R is pure semisimple if and only if every R-module is cyclically...

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.

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.

Addendum to .

Carl Faith (1998)

Publicacions Matemàtiques

Similarity:

Addendum to the author's article "Rings whose modules have maximal submodules", which appeared in Publicacions Matemàtiques 39, 1 (1995), 201-214.

On modules and rings with the restricted minimum condition

M. Tamer Koşan, Jan Žemlička (2015)

Colloquium Mathematicae

Similarity:

A module M satisfies the restricted minimum condition if M/N is artinian for every essential submodule N of M. A ring R is called a right RM-ring whenever R R satisfies the restricted minimum condition as a right module. We give several structural necessary conditions for particular classes of RM-rings. Furthermore, a commutative ring R is proved to be an RM-ring if and only if R/Soc(R) is noetherian and every singular module is semiartinian.

Modules with semiregular endomorphism rings

Kunio Yamagata (2008)

Colloquium Mathematicae

Similarity:

We characterize the semiregularity of the endomorphism ring of a module with respect to the ideal of endomorphisms with large kernel, and show some new classes of modules with semiregular endomorphism rings.