Vol. 107, No. 1, 1983

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Integral closure and generalized transforms in graded domains

Jon Lee Johnson

Vol. 107 (1983), No. 1, 173–178

In this article we consider the integral closure of integral domains by using the generalized transform and valuation rings. The first section establishes the basic theory in a general setting while the second deals with applications to graded rings, ending with a generalization of theorems due to Kuan and Seidenberg on integral closure in Z+ graded rings. As in a number of recent articles, we investigate the idea that if a property holds in the graded case, and it holds for Rs = {a∕ba,b R,b a homogeneous non-zero divisor}, then the property holds for the ring.

Mathematical Subject Classification 2000
Primary: 13B20, 13B20
Secondary: 13A05
Received: 7 October 1981
Published: 1 July 1983
Jon Lee Johnson