Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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QUASI-COMPLETENESS AND LOCALIZATIONS OF POLYNOMIAL DOMAINS: A CONJECTURE FROM "OPEN PROBLEMS IN COMMUTATIVE RING THEORY"

  • Received : 2014.11.14
  • Published : 2016.11.30
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Abstract

It is proved that $k[X_1,{\ldots},X_v ]$ localized at the ideal ($X_1,{\ldots},X_v$ ), where k is a field and $X_1,{\ldots},X_v$ indeterminates, is not weakly quasi-complete for $v{\geq}2$, thus proving a conjecture of D. D. Anderson and solving a problem from "Open Problems in Commutative Ring Theory" by Cahen, Fontana, Frisch, and Glaz.

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References

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  2. P.-J. Cahen, M. Fontana, S. Frisch, and S. Glaz, Open Problems in Commutative Ring Theory, In Fontana et al. (eds.), Commutative Algebra: Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions, Springer Verlag, New York, 2014.
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