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Root closure in integral domains, II

Published online by Cambridge University Press:  18 May 2009

David F. Anderson
David F. Anderson
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996, U.S.A.
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In this note, we give an elementary procedure for constructing n-root closed integral domains. We then use this construction to give two interesting examples. First, we give an example of a root closed integral domain which is not quasinormal. Secondly, we show that for any subset 5 of odd positive primes there is a one-dimensional affine domain which is p-root closed for a prime p if and only if p ∈ S.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 1 , January 1989 , pp. 127 - 130
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

References

1.Anderson, D. F., Root closure in integral domains, j. Algebra 79 (1982), 51–59.CrossRefGoogle Scholar
2.Anderson, D. F. and Dobbs, D. E., Fields in which seminormality implies normality, Houston J. Math., to appear.Google Scholar
3.Angermüller, G., On the root and integral closure of noetherian domains of dimension one, j. Algebra 83 (1983), 437–441.CrossRefGoogle Scholar
4.Angertnüller, G., Root closure, J. Algebra 90 (1984), 189–197.CrossRefGoogle Scholar
5.Brewer, J. W. and Costa, D. L., Seminormality and projective modules over polynomial rings, J. Algebra 58 (1979), 208–216.CrossRefGoogle Scholar
6.Brewer, J. W., Costa, D. L. and McCrimmon, K., Seminormality and root closure in polynomial rings and algebraic curves, J. Algebra 58 (1979), 217–226.CrossRefGoogle Scholar
7.Gilmer, R. and Heitmann, R. C., On Pic(R[X]) for R seminormal, J. Pure Appl. Algebra 16 (1980), 251–257.CrossRefGoogle Scholar
8.Onoda, N., Sugatani, T., and Yoshida, K., Local quasinormality and closedness type criteria, Houston J Math. 11 (1985), 247–256.Google Scholar
9.Onoda, N. and Yoshida, K., Remarks on quasinormal rings, j. Pure Appl. Algebra 33 (1984), 59–67.CrossRefGoogle Scholar
10.Lang, S., Algebra (Addison-Wesley, 1965).Google Scholar
11.Watkins, J. J., Root and integral closure for R[[X]], J. Algebra 75 (1982), 43–58.CrossRefGoogle Scholar