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Root Closure in Integral Domains, III

  • David F. Anderson (a1) and David E. Dobbs (a2)
Abstract

If A is a subring of a commutative ring B and if n is a positive integer, a number of sufficient conditions are given for “A[[X]] is n-root closed in B[[X]]” to be equivalent to “A is n-root closed in B.” In addition, it is shown that if S is a multiplicative submonoid of the positive integers ℙ which is generated by primes, then there exists a one-dimensional quasilocal integral domain A (resp., a von Neumann regular ring A) such that S = {n ∊ ℙ | A is n-root closed} (resp., S = {n ∊ ℙ | A[[X]] is n-root closed}).

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References
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1. Anderson, D. F., Root closure in integral domains. J. Algebra 79 (1982), 5159.
2. Anderson, D. F., Root closure in integral domains, II. Glasgow Math. J. 31 (1989), 127130.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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