FORMAL POWER SERIES RINGS OVER ZERO-DIMENSIONAL SFT-RINGS

Abstract

ABSTRACT: Let R be a zero-dimensional SFT-ring. It is proved that the minimal prime ideals of the formal power series ring A=R[[x1,..., xn]] are the ideals of the form M[[x1,..., xn]], whereM is a (minimal) prime of R. It follows that A has Krull dimension n and is catenarian. If R⊆T where T is also a zero-dimensional SFT-ring, the lying-over, going-up, incomparable, and going-down properties are studied for the extension A⊆T[[x1,..., xn]]. 1. Introduction. Throughout