Power series rings over discrete valuation rings

Jimmy T. Arnold

Vol. 93 (1981), No. 1, 31–33

DOI: 10.2140/pjm.1981.93.31

Abstract

If V is a discrete valuation ring with Krull dimension m, it is shown that the power series ring V [[x₁,⋯,x_n]] has Krull dimension mn + 1.

Mathematical Subject Classification 2000

Primary: 13F25

Secondary: 13A18

Milestones

Received: 19 March 1980

Revised: 25 August 1980

Published: 1 March 1981