From regular modules to von Neumann regular rings via coordinatization

2013/12/05 by Dăuş, Leonard, Mohamed Salim, Salim, Mohamed A.
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1312.1663

openalex publication_date 2013/12/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we establish a very close link (in terms of von Neumann's coordinatization) between regular modules introduced by Zelmanowitz, on one hand, and von Neumann regular rings, on the other hand: we prove that the lattice L^fg(M) of all finitely generated submodules of a finitely generated regular module M, over an arbitrary ring, can be coordinatized as the lattice of all principal right ideals of some von Neumann regular ring S.

Related

• Relative regular modules. Applications to von Neumann regular rings
• Biordered Sets of Regular Rings
• Coordinatization of lattices by regular rings without unit and Banaschewski functions
• Perspectivity in complemented modular lattices and regular rings
• \k₀ of semiartinian von Neumann regular rings. Direct\n finiteness versus unit-regularity