STRONGLY COMAXIMIZABLE PRIMES

[摘要] Let P be a prime ideal in an integral domain R with R lying between some Noetherian domain H and the integral closure of H. We call P strongly comaximizable if for every integer m greater-than-or-equal-to 1, there exists a finitely generated integral extension domain T of R such that T has exactly m primes lying over P, and those m primes are pairwise comaximal. We show that if P is not contained in the Jacobson radical of R, then P is strongly comaximizable. We also show that if P is not strongly comaximizable and R is either integrally closed or quasi-local, then P satisfies a certain ''Henselian like'' property. (C) 1994 Academic Press, Inc.

[发布日期] 1994-11-15