Subanillos reticulados convexos de f-anillos von Neumann regulares

Convex Lattice-Ordered Subrings of von Neumann Regular f-Rings

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. Tambien se da una version real cerrada de
este resultado.

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.

Convex Lattice-Ordered Subrings of von Neumann Regular f-Rings Subanillos reticulados convexos de f-anillos von Neumann regulares JORGE I. GUIER¹

¹Universidad de Costa Rica, San José, Costa Rica. Email: jorge.guier@ucr.ac.cr

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Abstract

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.

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2000 Mathematics Subject Classification: 13J25, 06E20.

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Resumen

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.

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Texto completo disponible en PDF

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References

[1] M. F. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley, Reading, 1969.

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(Recibido en noviembre de 2014. Aceptado en mayo de 2015)

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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}
}

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