Note generalizing a result of Samuel’s

Luther Elic Claborn

Vol. 15 (1965), No. 3, 805–808

DOI: 10.2140/pjm.1965.15.805

Abstract

Let C(A) denote the class group of a Krull domain A. Samuel has established (a) C(A) → C(A[[X₁,⋯,X_n]]) is injective, and (b) C(A) → C(A[[X₁,⋯,X_n]]) is bijective in Case A is a regular U.F.D. This note establishes that C(A) → C(A[[X₁,⋯,X_n]]) is bijective in Case A is a regular noetherian domain, thus adding a complement to (a) while generalizing (b). A corollary of this is that A[[X₁,⋯,X_n]]_S is a U.F.D. if A is a regular Noetherian domain and S is the set of nonzero elements of A.

Mathematical Subject Classification

Primary: 13.93

Secondary: 13.20

Milestones

Received: 17 July 1964

Published: 1 September 1965