Displaying similar documents to “Modules whose countably generated submodules are epimorphic images”

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.

Perfect rings for which the converse of Schur's lemma holds.

Abdelfattah Haily, Mostafa Alaoui (2001)

Publicacions Matemàtiques

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If M is a simple module over a ring R then, by the Schur's lemma, the endomorphism ring of M is a division ring. However, the converse of this result does not hold in general, even when R is artinian. In this short note, we consider perfect rings for which the converse assertion is true, and we show that these rings are exactly the primary decomposable ones.

Rings whose modules are finitely generated over their endomorphism rings

Nguyen Viet Dung, José Luis García (2009)

Colloquium Mathematicae

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A module M is called finendo (cofinendo) if M is finitely generated (respectively, finitely cogenerated) over its endomorphism ring. It is proved that if R is any hereditary ring, then the following conditions are equivalent: (a) Every right R-module is finendo; (b) Every left R-module is cofinendo; (c) R is left pure semisimple and every finitely generated indecomposable left R-module is cofinendo; (d) R is left pure semisimple and every finitely generated indecomposable left R-module...

Steady ideals and rings

Jan Žemlička, Jan Trlifaj (1997)

Rendiconti del Seminario Matematico della Università di Padova

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Isomorphism Theorem on Vector Spaces over a Ring

Yuichi Futa, Yasunari Shidama (2017)

Formalized Mathematics

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In this article, we formalize in the Mizar system [1, 4] some properties of vector spaces over a ring. We formally prove the first isomorphism theorem of vector spaces over a ring. We also formalize the product space of vector spaces. ℤ-modules are useful for lattice problems such as LLL (Lenstra, Lenstra and Lovász) [5] base reduction algorithm and cryptographic systems [6, 2].