J Austral Math Soc Ser A 55 pp238--245, 1993.

Pairs of Rings with a Bijective Correspondence Between the Prime Spectra

E. Jespers and P. Wauters

Abstract

Let A be a subring of a commutative ring B. If the natural mapping from the prime spectrum of B to the prime spectrum of A is injective (respectively bijective) then the pair (A, B) is said to have the injective (respectively bijective) Spec-map. We give necessary and sufficient conditions for a pair of rings A and B graded by a free abelian group to have the injective (respectively bijective) Spec-map. For this we first deal with the polynomial case. Let l be a field and k be a subfield. Then the pair of polynomial rings (k[X], l[X]) has the injective Spec-map if and only if l is a purely inseperable extension of k.

1991 AMS Subject Classification: 13A17, 13B25, 16A03

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Authors

E. Jespers

Memorial University of Newfoundland, St. John's, Newfoundland, Canada A1C 5S7.

P. Wauters

Economishe Hogeschool Limburg and Limburgs Universitair Centrum, 3590 Diepenbeek Belgium.