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Prime ideals in power series rings

Part of the Lecture Notes in Mathematics book series (LNM,volume 311)

Abstract

In this paper we wish to briefly review some known results concerning the ideal structure of the formal power series ring R[[X]]. As the title indicates, primary consideration will be given to prime ideals in R[[X]]. We begin by discussing some of the basic difficulties which arise in relating the ideal structure of R[[X]] with that of R. We then consider the Krull dimension of R[[X]] and, finally, we review some results on valuation overrings of D[[X]], where D is an integral domain.

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References

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© 1973 Springer-Verlag

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Arnold, J.T. (1973). Prime ideals in power series rings. In: Brewer, J.W., Rutter, E.A. (eds) Conference on Commutative Algebra. Lecture Notes in Mathematics, vol 311. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068915

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  • DOI: https://doi.org/10.1007/BFb0068915

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06140-3

  • Online ISBN: 978-3-540-38340-6

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