Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Two notes on imbedded prime divisors


Author: L. J. Ratliff
Journal: Proc. Amer. Math. Soc. 101 (1987), 395-402
MSC: Primary 13A17; Secondary 13E05
MathSciNet review: 908637
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The first note shows that if $ R < T$ are any two Noetherian rings, then there exists a Noetherian ring $ B$ between $ R$ and $ T$ which has a maximal ideal $ N$ such that $ {\text{grade}}(N) \leq 1$ and $ N \cap R$ is a maximal ideal. The second note shows that if $ R$ is a Noetherian ring, then there exists a free quadratic integral extension ring $ B$ of $ R$ such that $ \operatorname{Spec}(B) \cong \operatorname{Spec}(R)$ and such that if $ I$ is any regular ideal in $ R$ and $ {P_1} \cap \cdots \cap {P_g}$ are prime ideals in $ R$ containing $ I$, then there exists an ideal $ J$ in $ B$ integrally dependent on $ IB$ such that the prime ideals corresponding to the $ {P_i}$ are prime divisors of $ {J^n}$ for all $ n \geq 1$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13A17, 13E05

Retrieve articles in all journals with MSC: 13A17, 13E05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0908637-1
PII: S 0002-9939(1987)0908637-1
Keywords: Cohen-Macaulay ring, flat extension ring, grade of an ideal, integral closure of an ideal, integral extension ring, Notherian ring, prime divisor semilocal ring
Article copyright: © Copyright 1987 American Mathematical Society