Symbolic powers of prime ideals and their topology

Schenzel, Peter

doi:10.1090/S0002-9939-1985-0766518-9

Symbolic powers of prime ideals and their topology
HTML articles powered by AMS MathViewer

by Peter Schenzel PDF

Proc. Amer. Math. Soc. 93 (1985), 15-20 Request permission

Abstract:

For a prime ideal $P$ of a commutative Noetherian ring $R$ a necessary and sufficient condition is given to determine when the $P$-adic topology is equivalent, resp. linearly equivalent, to the $P$-symbolic topology. The last means that the symbolic Rees ring is a finitely generated module over the ordinary Rees ring of $P$. Then it is considered when the integral closure of all the powers of $P$ are primary.

References

M. Brodmann, Asymptotic stability of $\textrm {Ass}(M/I^{n}M)$, Proc. Amer. Math. Soc. 74 (1979), no. 1, 16–18. MR 521865, DOI 10.1090/S0002-9939-1979-0521865-8
Markus P. Brodmann, Finiteness of ideal transforms, J. Algebra 63 (1980), no. 1, 162–185. MR 568570, DOI 10.1016/0021-8693(80)90031-9
Robin Hartshorne, Affine duality and cofiniteness, Invent. Math. 9 (1969/70), 145–164. MR 257096, DOI 10.1007/BF01404554
Craig Huneke, On the associated graded ring of an ideal, Illinois J. Math. 26 (1982), no. 1, 121–137. MR 638557

Prime divisors, asymptotic

-sequences and unmixed local rings

Stephen McAdam, Asymptotic prime divisors and analytic spreads, Proc. Amer. Math. Soc. 80 (1980), no. 4, 555–559. MR 587926, DOI 10.1090/S0002-9939-1980-0587926-0
Stephen McAdam, Asymptotic prime divisors and going down, Pacific J. Math. 91 (1980), no. 1, 179–186. MR 612897
L. J. Ratliff Jr., On prime divisors of $I^{n},$ $n$ large, Michigan Math. J. 23 (1976), no. 4, 337–352 (1977). MR 457421
L. J. Ratliff Jr., On asymptotic prime divisors, Pacific J. Math. 111 (1984), no. 2, 395–413. MR 734863
D. Rees, A note on analytically unramified local rings, J. London Math. Soc. 36 (1961), 24–28. MR 126465, DOI 10.1112/jlms/s1-36.1.24
Peter Schenzel, Independent elements, unmixedness theorems, and asymptotic prime divisors, J. Algebra 92 (1985), no. 1, 157–170. MR 772477, DOI 10.1016/0021-8693(85)90151-6