Displaying similar documents to “О модельной полноте некоторых теорий модулей.”

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.

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].