1Universidad de Costa Rica, San José, Costa Rica. Email: jorge.guier@ucr.ac.cr
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.
Key words: Lattice-ordered ring, projectable f-ring, von Neumann regular ring, convex subring, first convexity property, real closed ring, ring of quotients, valuation ring.
El propósito de este artículo es caracterizar los subanillos convexos de los f-anillos von Neumann regulares. Estos son los f-anillos reducidos, proyectables y que satisfacen la propiedad de convexidad, i.e.: para todo a, b, si 0 < a < b entonces b divide a. También se da una versión real cerrada de este resultado.
Palabras clave: Anillo reticulado, f-anillo proyectable, anillo von Neumann regular, subanillo convexo, primera propiedad de convexidad, anillo real cerrado, anillo de cocientes, anillo de valuación.
Texto completo disponible en PDF
References
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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCMv49n1a08,
AUTHOR = {Guier, Jorge I.},
TITLE = {{Convex Lattice-Ordered Subrings of von Neumann Regular \boldsymbol{f}-Rings}},
JOURNAL = {Revista Colombiana de Matemáticas},
YEAR = {2015},
volume = {49},
number = {1},
pages = {161--170}
}