Vol. 18, No. 2, 1966

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A note on the class group

Luther Elic Claborn

Vol. 18 (1966), No. 2, 223–225

The main result yields some information on the class group of a domain R in terms of the class group of R∕xR. With slightly stronger hypotheses than are strictly necessary, we state the main result: Let R be a regular domain, x a prime element contained in the radical of R, and suppose that R∕xR is locally a unique factorization domain. Let {Iα} be a set of unmixed height 1 ideals of R such that the classes of {Iα + xR∕xR} generate the class group of R∕xR; then the classes of {Iα} generate the class group of R.

Mathematical Subject Classification
Primary: 13.20
Received: 29 April 1965
Published: 1 August 1966
Luther Elic Claborn