Fraction-Dense Algebras and Spaces

Hager, Anthony W. ; Martinez, Jorge

Canadian journal of mathematics, Tome 45 (1993) no. 5, pp. 977-996

Résumé

A fraction-dense (semi-prime) commutative ring A with 1 is one for which the classical quotient ring is rigid in its maximal quotient ring. The fractiondense ƒ- rings are characterized as those for which the space of minimal prime ideals is compact and extremally disconnected. For archimedean lattice-ordered groups with this property it is shown that the Dedekind and order completion coincide. Fractiondense spaces are defined as those for which C(X) is fraction-dense. If X is compact, then this notion is equivalent to the coincidence of the absolute of X and its quasi-F cover. R-embeddings of Tychonoff spaces are re-introduced and examined in the context of fraction-density.

Détail

DOI : 10.4153/CJM-1993-054-6

Mots-clés : 06F25, 54C40

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