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Chain conjectures and H-domains

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

Abstract

Some new equivalences to the chain conjecture (the integral closure of a local domain is catenary) and to the catenary chain conjecture (the integral closure of a catenary local domain is catenary) are proved, as are some new characterizations of a local H-domain. Also, a fact which lends support to the chain conjecture is noted, and it is proved that the H-conjecture (a local H-domain is catenary) implies the catenary chain conjecture.

Keywords

  • Prime Ideal
  • Maximal Ideal
  • Integral Domain
  • Local Domain
  • Chain Condition

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Research on this paper was supported in part by the National Science Foundation, Grant 28939.

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© 1973 Springer-Verlag

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Ratliff, L.J. (1973). Chain conjectures and H-domains. 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/BFb0068931

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  • DOI: https://doi.org/10.1007/BFb0068931

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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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