E. Jespers et P. Wauters, PAIRS OF RINGS WITH A BIJECTIVE CORRESPONDENCE BETWEEN THE PRIME SPECTRA, Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics, 55, 1993, pp. 238-245
Citations number
5
Categorie Soggetti
Mathematics, General","Statistic & Probability",Mathematics,"Statistic & Probability
Let A be a subring of a commutative ring B. If the natural mapping fro
m the prime spectrum of B to the prime spectrum of A is injective (res
pectively bijective) then the pair (A, B) is said to have the injectiv
e (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 f
irst 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.