Asymptotic prime divisors and analytic spreads

Author:
Stephen McAdam

Journal:
Proc. Amer. Math. Soc. **80** (1980), 555-559

MSC:
Primary 13E05

DOI:
https://doi.org/10.1090/S0002-9939-1980-0587926-0

MathSciNet review:
587926

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let *I* be an ideal in a Noetherian domain *R*, and let *Î* be the integral closure of *I*. Let for *n* large (it being known that for large *n* this set does not vary with *n*). Suppose that *R* satisfies the altitude formula. Then it is shown that if and only if height , the analytic spread of .

**[1]**M. Brodmann,*Asymptotic stability of*, Proc. Amer. Math. Soc.**74**(1979), 16-18. MR**521865 (80c:13012)****[2]**-,*The asymptotic nature of the analytic spread*(preprint).**[3]**I. Kaplansky,*Commutative rings*, rev. ed., Univ. of Chicago Press, Chicago, Ill., 1974. MR**0345945 (49:10674)****[4]**S. McAdam and E. Davis,*Prime divisors and saturated chains*, Indiana Univ. Math. J.**26**(1977), 653-662. MR**0444633 (56:2983)****[5]**S. McAdam and P. Eakin,*The asymptotic*Ass, J. Algebra**61**(1979), 71-81. MR**554852 (81f:13001)****[6]**M. Nagata,*Local rings*, Interscience, New York, 1962. MR**0155856 (27:5790)****[7]**D. G. Northcott and D. Rees,*Reductions of ideals in local rings*, Proc. Cambridge Philos. Soc.**50**(1954), 145-158. MR**0059889 (15:596a)****[8]**-,*A note of reductions of ideals with an application to the generalized Hilbert function*, Proc. Cambridge Philos. Soc.**50**(1954), 353-359. MR**0062115 (15:929e)****[9]**L. J. Ratliff, Jr.,*On prime divisors of*,*n large*, Michigan Math. J.**23**(1976), 337-352. MR**0457421 (56:15626)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
13E05

Retrieve articles in all journals with MSC: 13E05

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1980-0587926-0

Keywords:
Noetherian domain,
prime divisors,
analytic spread,
integral closure of an ideal

Article copyright:
© Copyright 1980
American Mathematical Society