Abstract

GUIER, JORGE I.. Convex Lattice-Ordered Subrings of von Neumann Regular f-Rings. Rev.colomb.mat. [online]. 2015, vol.49, n.1, pp.161-170. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v49n1.54177.

The purpose of this paper is to characterize the lattice-ordered convex subrings of von Neumann regular f-rings. They turn out to be the reduced projectable f-rings satisfying the convexity property, i.e.: for all a, b, if 0 < a < b then b divides a. A real closed version of this result can also be stated.

Keywords : Lattice-ordered ring; projectable f-ring; von Neumann regular ring; convex subring; first convexity property; real closed ring; ring of quotients; valuation ring.

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