Contribution to the study of lattice-ordered rings and f-rings.

Autores: Joan Trias Pairó
Localización: Stochastica: revista de matemática pura y aplicada, ISSN 0210-7821, Vol. 3, Nº. 2, 1979, págs. 45-69
Idioma: español
Títulos paralelos:
- Contribución al estudio de los anillos reticulados y f-anillos.
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Resumen
- This paper deals with ordered rings and f-rings. Some relations between classes of ideals are obtained. The idea of subunity allows us to study the possibility of embedding the ring in a unitary f-ring. The Boolean algebras of idempotents and lattice-isometries in an f-ring are studied. We give geometric characterizations of the l-isometries and obtain, in the projectable case, that the Stone space of the Boolean algebra of l-isometries is homeomorphic to the space of minimal prime ideals with the hull-kernel topology. We also apply some results to a certain f-ring of Hermitian operators of a Hilbert space.