Three theorems on form rings

Author:
Louis J. Ratliff

Journal:
Proc. Amer. Math. Soc. **99** (1987), 432-436

MSC:
Primary 13E05; Secondary 13A17, 13C15

DOI:
https://doi.org/10.1090/S0002-9939-1987-0875376-5

MathSciNet review:
875376

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Abstract | References | Similar Articles | Additional Information

Abstract: Three theorems concerning the form ring (= associated graded ring) of an ideal in a Noetherian ring are proved. The first characterizes, for a -primary ideal in a locally quasi-unmixed ring, when is an integral domain in terms of when is an integral domain. For an aribtrary Noetherian ring the second gives a somewhat similar characterization for to have only one prime divisor of zero for some ideal that is projectively equivalent to . And the third characterizes unmixed semilocal rings in terms of the existence of an open ideal such that the zero ideal in is isobathy.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1987-0875376-5

Keywords:
Analytically unramified semilocal ring,
asymptotic prime divisor,
analytic spread of an ideal,
essential prime divisor,
form ring,
integral closure of an ideal,
isobathy ideal,
Noetherian ring,
normal ideal,
projectively equivalent ideals,
quasi-unmixed local ring,
Rees ring,
unmixed local ring,
-essential prime divisor

Article copyright:
© Copyright 1987
American Mathematical Society