Daus, Leonard; Salim, Mohamed A. From regular modules to von Neumann regular rings via coordinatization. (English) Zbl 1313.16021 Rom. J. Math. Comput. Sci. 4, No. 2, 125-130 (2014). Summary: 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 \(\mathcal L^{fg}(M)\) 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 \(S\). MSC: 16E50 von Neumann regular rings and generalizations (associative algebraic aspects) 16D25 Ideals in associative algebras 06C20 Complemented modular lattices, continuous geometries 06D05 Structure and representation theory of distributive lattices Keywords:coordinatization; regular modules; von Neumann regular rings; complemented modular lattices; distributive lattices; lattices of submodules; lattices of right ideals PDFBibTeX XMLCite \textit{L. Daus} and \textit{M. A. Salim}, Rom. J. Math. Comput. Sci. 4, No. 2, 125--130 (2014; Zbl 1313.16021) Full Text: arXiv