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Progress on the dimension question for power series rings

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Multiplicative Ideal Theory in Commutative Algebra

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References

  1. J. Arnold.: Krull dimension in power series rings. Trans. Amer. Math. Soc. 177, 299–304 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Arnold.: Power series rings over discrete valuation rings. Pacific J. Math. 93, 31–33 (1981)

    MathSciNet  MATH  Google Scholar 

  3. J. Arnold.: Power series rings with finite Krull dimension. Indiana Univ. Math. J. 31, 897–911 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Arnold and J. Brewer.: When (D[[X]]) P[[X]] is a valuation ring. Proc. Amer. Math. Soc. 37, 326–332 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  5. J. Brewer.: Power series over commutative rings. Dekker, (1981)

    Google Scholar 

  6. J. Condo, J. Coykendall.: Strong convergence properties of SET rings. Comm. Algebra 27, 2073–2085 (1999)

    MathSciNet  MATH  Google Scholar 

  7. J. Condo, J Coykendall, D. Dobbs.: Formal power series rings over zerodimensional SFT-rings. Comm. Algebra 24, 2687–2698 (1996)

    MathSciNet  MATH  Google Scholar 

  8. J. Coykendall.: The SFT property does not imply finite dimension for power series rings. J. Algebra 256, 85–96 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. J. Coykendall, D. Dobbs.: Fragmented domains have infinite KruU dimension. Rend. Circ. Mat. Palermo 50, 377–388 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. D. Fields.: Dimension theory in power series rings. Pacific J. Math. 35, 326–332 (1970)

    MathSciNet  Google Scholar 

  11. R. Gilmer.: Dimension theory of power series rings over a commutative ring. Algebra and logic (Fourteenth Summer Res. Inst., Austral. Math. Soc, Monash Univ., Clayton, 1974), Lecture Notes in Math., Vol. 450. Springer, Berlin Heidelberg New York, 155–162 (1975)

    Google Scholar 

  12. B. Kang and M. Park. A localization of a power series ring over a valuation domain. J. Pure Appl. Algebra 140, 107–124 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  13. B. Kang and M. Park. Krull dimension in power series rings. Preprint.

    Google Scholar 

  14. I. Kaplansky. Commutative Rings. University of Chicago Press, Chicago (1974)

    MATH  Google Scholar 

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Coykendall, J. (2006). Progress on the dimension question for power series rings. In: Brewer, J.W., Glaz, S., Heinzer, W.J., Olberding, B.M. (eds) Multiplicative Ideal Theory in Commutative Algebra. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-36717-0_8

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