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On the complete integral closure of an integral domain

Published online by Cambridge University Press:  09 April 2009

Robert W. Gilmer Jr  and
William J. Heinzer
Robert W. Gilmer Jr
Affiliation:
Florida State University Tallahassee, Florida
William J. Heinzer
Affiliation:
Florida State University Tallahassee, Florida
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We consider in this paper only commutative rings with identity. When R is considered as a subring of S it will always be assumed that R and S have the same identity. If R is a subring of S an element s of S said to be integral over R if s is the root of a monic polynomial with coefficients in R. Following Krull [8], p. 102, we say s is almost integral over R provided all powers of s belong to a finite R-submodule of S. If R1 is the set of elements of S almost integral over R we say R1 is the complete integral closure of R in S.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 6 , Issue 3 , August 1966 , pp. 351 - 361
Copyright
Copyright © Australian Mathematical Society 1966

References

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