Chain of prime ideals in formal power series rings

Authors:
Ada Maria de S. Doering and Yves Lequain

Journal:
Proc. Amer. Math. Soc. **88** (1983), 591-594

MSC:
Primary 13A15; Secondary 13C15, 13F25, 13J10

DOI:
https://doi.org/10.1090/S0002-9939-1983-0702281-3

MathSciNet review:
702281

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a Noetherian domain and a prime ideal of . Then has a maximal chain of prime ideals of length if and only if does, if and only if does.

**[1]**J. T. Arnold,*Krull dimension in power series rings*, Trans. Amer. Math. Soc.**177**(1973), 299-304. MR**0316451 (47:4998)****[2]**-,*Algebraic extensions of power series rings*, Trans. Amer. Math. Soc.**267**(1981), 95-110. MR**621975 (82k:13025)****[3]**J. T. Arnold and D. W. Boyd,*Transcendence degree in power series rings*, J. Algebra**57**(1979), 180-195. MR**533108 (82k:13024)****[4]**Y. Lequain,*Catenarian property in a domain of formal power series*, J. Algebra**65**(1980), 110-117. MR**578799 (81g:13009)****[5]**M. Nagata,*Local rings*, Interscience, New York, 1962. MR**0155856 (27:5790)****[6]**L. Ratliff and S. McAdam,*Maximal chains of prime ideals in integral extension domains*. I, Trans. Amer. Math. Soc.**224**(1976), 103-116. MR**0437513 (55:10438a)****[7]**P. B. Sheldon,*How changing**changes its quotient field*, Trans. Amer. Math. Soc.**159**(1971), 223-244. MR**0279092 (43:4818)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
13A15,
13C15,
13F25,
13J10

Retrieve articles in all journals with MSC: 13A15, 13C15, 13F25, 13J10

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0702281-3

Keywords:
Chain of prime ideals,
formal power series ring,
polynomial ring,
localization

Article copyright:
© Copyright 1983
American Mathematical Society