Keywords
elementary class
continuous sections
Baer rings
PP-rings
minimal prime ideales
productos booleanos
clases elementales
secciones continuas
anillos de Baer
PP-anillos
ideales primos minimales
How to Cite
Abstract
Keimel introduced the notion of proyectability in the class of lattice-ordered rings and f-rings in [5]. Here we introduce a similar notion forgeting the lattice and ordered structure of the ring and interpretating the orthogonality within the multiplicative structure (in the class of reduced rings). This notion turns out to be equivalent to the one defining the class of PP-rings and it is related to the compactness of the space of the minimal primes ideals and to the class of weak Baer rings.
References
Chang, C.C.; Keisler, H.J. (1978) Model Theory. North-Holland, Amsterdam.
Guier, J.I. (2001) “Boolean products of real closed valuation rings and fields”, Annals of Pure and Applied Logic 112: 119–150.
Henriksen, M.; Jerison, M. (1965) “The space of minimal prime ideals of a commutative ring”, Trans. Amer. Math. Soc. 115: 110–130.
Höchster, M. (1970) “Totally integrally closed rings and extremal spaces”, Pacific J. Math. 32: 767–779.
Keimel, K. (1971) The Representation of Lattice-Ordered Groups and Rings by Sections of Sheaves. Lectures Notes in Mathematics 248, Springer-Verlag, Berlin Heidelberg: 1-98.
Kist, J. (1974) “Two characterizations for conmutative Baer rings”, Pacific J. Math. 50: 125–134.
Ewad Abu Osba; Al-Ezeh, H. (2004) “The pure part of the ideals in C(X)”, preprint.
Picavet, G. (1980) “Ultrafiltres sur un espace spectral – Anneaux de Baer – Anneaux a spectre minimal compact”, Math. Scand. 46: 23–53.
Weispfenning, V. (1973) “Model-completeness and elimination of quantifiers for subdirect products of structures”, Journal of Algebra 36: 252–277.