Dimension theory in power series rings

David E. Fields

Vol. 35 (1970), No. 3, 601–611

DOI: 10.2140/pjm.1970.35.601

Abstract

Let V be a valuation ring of finite rank n. If V is discrete, then V [[X]] has dimension n + 1. If V is not discrete, then the dimension of V [[X]] is at least n + k + 1, where k is the number of idempotent proper prime ideals of V .

Mathematical Subject Classification

Primary: 13.93

Milestones

Received: 12 May 1970

Published: 1 December 1970