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

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Abstract: The first note shows that if are any two Noetherian rings, then there exists a Noetherian ring between and which has a maximal ideal such that and is a maximal ideal. The second note shows that if is a Noetherian ring, then there exists a free quadratic integral extension ring of such that and such that if is any regular ideal in and are prime ideals in containing , then there exists an ideal in integrally dependent on such that the prime ideals corresponding to the are prime divisors of for all .

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DOI:
https://doi.org/10.1090/S0002-9939-1987-0908637-1

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