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On Integral Closure

Published online by Cambridge University Press:  20 November 2018

Hubert Butts ,
Marshall Hall Jr.  and
H. B. Mann
Hubert Butts
Affiliation:
Louisiana State University
Marshall Hall Jr.
Affiliation:
Ohio State University
H. B. Mann
Affiliation:
Ohio State University
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Let J be an integral domain (i.e., a commutative ring without divisors of zero) with unit element, F its quotient field and J[x] the integral domain of polynomials with coefficients from J . The domain J is called integrally closed if every root of a monic polynomial over J which is in F also is in J.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 471 - 473
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Hecke, Erich, Vorlesungen ueber die Theorie der algebraischen Zahlen (New York, 1948).Google Scholar
2. van der Waerden, B. L., Modern Algebra, Vol. 1 (New York, 1949).Google Scholar
3. Weyl, Herman, Algebraic Theory of Numbers (Princeton, 1940).Google Scholar