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Pairs of rings with a bijective correspondence between the prime spectra

Part of: Ring extensions and related topics

Published online by Cambridge University Press:  09 April 2009

E. Jespers  and
P. Wauters
E. Jespers
Affiliation:
Memorial University of Newfoundland, St. John's, NewfoundlandCanada, A1C 5S7
P. Wauters
Affiliation:
Economische Hogeschool Limburg, and Limburgs Universitair Centrum, 3590 Diepenbeek, Belgium
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Abstract

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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 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 inseparable extension of k.

MSC classification

Secondary: 13B25: Polynomials over commutative rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 55 , Issue 2 , October 1993 , pp. 238 - 245
Copyright
Copyright © Australian Mathematical Society 1993

References

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