Vol. 15, No. 3, 1965

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Note generalizing a result of Samuel’s

Luther Elic Claborn

Vol. 15 (1965), No. 3, 805–808

Let C(A) denote the class group of a Krull domain A. Samuel has established (a) C(A) C(A[[X1,,Xn]]) is injective, and (b) C(A) C(A[[X1,,Xn]]) is bijective in Case A is a regular U.F.D. This note establishes that C(A) C(A[[X1,,Xn]]) 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,,Xn]]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
Received: 17 July 1964
Published: 1 September 1965
Luther Elic Claborn