Root closure in integral domains, II
Glasgow mathematical journal, Tome 31 (1989) no. 1, pp. 127-130

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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.
Anderson, David F. Root closure in integral domains, II. Glasgow mathematical journal, Tome 31 (1989) no. 1, pp. 127-130. doi: 10.1017/S0017089500007618
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[1] 1.Anderson, D. F., Root closure in integral domains, j. Algebra 79 (1982), 51–59. Google Scholar | DOI

[2] 2.Anderson, D. F. and Dobbs, D. E., Fields in which seminormality implies normality, Houston J. Math., to appear. Google Scholar

[3] 3.Angermüller, G., On the root and integral closure of noetherian domains of dimension one, j. Algebra 83 (1983), 437–441. Google Scholar | DOI

[4] 4.Angertnüller, G., Root closure, J. Algebra 90 (1984), 189–197. Google Scholar | DOI

[5] 5.Brewer, J. W. and Costa, D. L., Seminormality and projective modules over polynomial rings, J. Algebra 58 (1979), 208–216. Google Scholar | DOI

[6] 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. Google Scholar | DOI

[7] 7.Gilmer, R. and Heitmann, R. C., On Pic(R[X]) for R seminormal, J. Pure Appl. Algebra 16 (1980), 251–257. Google Scholar | DOI

[8] 8.Onoda, N., Sugatani, T., and Yoshida, K., Local quasinormality and closedness type criteria, Houston J Math. 11 (1985), 247–256. Google Scholar

[9] 9.Onoda, N. and Yoshida, K., Remarks on quasinormal rings, j. Pure Appl. Algebra 33 (1984), 59–67. Google Scholar | DOI

[10] 10.Lang, S., Algebra (Addison-Wesley, 1965). Google Scholar

[11] 11.Watkins, J. J., Root and integral closure for R[[X]], J. Algebra 75 (1982), 43–58. Google Scholar | DOI

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