Pairs of rings with a bijective correspondence between the prime spectra

Journal of the Australian Mathematical Society

E. Jespers¹ 

[1] P. Wauters

关键词: 13 A 17;    13 B 25;    16 A 03;   

DOI  :  10.1017/S1446788700032055

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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.

【 授权许可】

Unknown