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Dimension theory of power series rings over a commutative ring

Part of the Lecture Notes in Mathematics book series (LNM,volume 450)

Abstract

This paper is a survey of some known results concerning the dimension theory of power series rings in finitely many indeterminates over a commutative ring with identity.

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Bibliography

  1. ARNOLD, J.T. Prime ideals in power series rings, Conference on Commutative Algebra Proceedings 1972, Lecture Notes in Mathematics #311, Springer-Verlag, New York, 1972.

    Google Scholar 

  2. Power series rings over Prüfer domains, Pacific J. Math. 44, 1–11, 1973.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Krull dimension in power series rings, Trans. Amer. Math. Soc. 177, 1973, 299–304.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. ARNOLD, J.T. and J.W. BREWER On when (D[[X]])P[[X]] is a valuation ring, Proc. Amer. Math. Soc. 37, 326–332, 1973.

    MathSciNet  MATH  Google Scholar 

  5. FIELDS, D.E. Dimension theory in power series rings, Pacific J. Math. 35, 601–611, 1970.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. GILMER, R. A note on the quotient field of the domain D[[X]], Proc. Amer. Math. Soc. 18, 1138–1140, 1967.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. RIVET, R. Sur le corps de fractions d'un anneau de séries formelles à coefficients dans un anneau de valuation discrète, C.R. Paris Acad. Sci. Sér. A 264, 1047–1049, 1967.

    MathSciNet  MATH  Google Scholar 

  8. Sur les fonctions à valeurs entières, associées au corps des fractions d'un anneau de séries formelles à coefficients dans un anneau de valuation discrète, C.R. Paris Acad. Sci. Sér. A 268, 1455–1457, 1969.

    MathSciNet  MATH  Google Scholar 

  9. Famille d'anneaux locaux henseliens dominés par Cf(A)[[X]], défines par des fonctions pseudo-concaves, C.R. Paris Acad. Sci. Sér. A 272, 369–371, 1971.

    MathSciNet  MATH  Google Scholar 

  10. SHELDON, P. How changing D[[X]] changes its quotient field, Trans. Amer. Math. Soc. 159, 223–244, 1971.

    MathSciNet  MATH  Google Scholar 

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© 1975 Springer-Verlag

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Gilmer, R. (1975). Dimension theory of power series rings over a commutative ring. In: Crossley, J.N. (eds) Algebra and Logic. Lecture Notes in Mathematics, vol 450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062854

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  • DOI: https://doi.org/10.1007/BFb0062854

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07152-5

  • Online ISBN: 978-3-540-37480-0

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