Maximal chains of prime ideals in integral extension domains. II

Ratliff, L. J.

doi:10.1090/S0002-9947-1976-0437514-5

Maximal chains of prime ideals in integral extension domains. II
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Trans. Amer. Math. Soc. 224 (1976), 117-141 Request permission

Abstract:

Four related subjects are investigated: (1) If (L, N) is a locality over a local domain (R, M) such that $N \cap R = M$, and if there exists an integral extension domain of L which has a maximal chain of prime ideals of length n (for short, a mcpil n), then there exists an integral extension domain of R which has a mcpil $n - {\text {trd}}\;L/R + {\text {trd}}(L/N)/(R/M)$. A refinement of the altitude inequality follows from this. (2) A condition for the converse of (1) to hold is given. (3) The class of local domains R such that there exists an integral extension domain of R which has a mcpil n if and only if there exists a mcpil n in R is studied. (4) Two new equivalences for the existence of mcpil n in an integral extension domain of a local domain are given.

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