Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-24T15:03:45.137Z Has data issue: false hasContentIssue false
  • English
  • Français

Localizations of Hi and Di Rings

Published online by Cambridge University Press:  20 November 2018

Evan G. Houston
Evan G. Houston*
Affiliation:
University of North Carolina at Charlotte, Charlotte, North Carolina
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we study conditions under which certain localizations of semilocal Hi and Di rings satisfy the second chain condition. Two of these results are as follows.

  • 1) If P is a prime in a semilocal Hi ring with depth P > i ≧ height P — 1, then RP satisfies the second chain condition.

    2) If P is a prime in a semilocal Dt ring with depth P ≧ i, then RP satisfies the second chain condition.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 4 , 01 August 1976 , pp. 815 - 819
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Houston, E. G. and McAdam, S., Chains of primes in noeiherian rings, Indiana University Math. J. 24 (1975), 741–753.Google Scholar
2. Kaplansky, I., Commutative rings (Allyn and Bacon, Boston, 1970).Google Scholar
3. McAdam, S., Saturated chains in noetherian rings, Indiana Univ. Math. J. 23 (1974), 719–728.Google Scholar
4. McAdam, S. and Ratliff, L. J., Jr., Semi-local taut rings, manuscript.Google Scholar
5. McAdam, S. and Ratliff, L. J., Jr., Polynomial rings and Hi-local rings (II), manuscript.Google Scholar
6. Pettit, M. E., Properties of Hi-rings, Ph.D. Thesis, Univ. of California at Riverside, 1973.Google Scholar
7. Ratliff, L. J., Jr., On quasi-unmixed local domains, the altitude formula, and the chain condition for prime ideals (I), Amer. J. Math. 01 (1969), 508–528.Google Scholar
8. Ratliff, L. J., Jr., Characterizations of catenary rings, Amer. J. Math. 1)3 (1971), 1070–1108.Google Scholar