Every local ring is dominated

by a one-dimensional local ring

Authors:
Robert Gilmer and William Heinzer

Journal:
Proc. Amer. Math. Soc. **125** (1997), 2513-2520

MSC (1991):
Primary 13B02, 13C15, 13E05, 13H99

DOI:
https://doi.org/10.1090/S0002-9939-97-03847-1

MathSciNet review:
1389520

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a local (Noetherian) ring. The main result of this paper asserts the existence of a local extension ring of such that (i) dominates , (ii) the residue field of is a finite purely transcendental extension of , (iii) every associated prime of (0) in contracts in to an associated prime of (0), and (iv) . In addition, it is shown that can be obtained so that either is the maximal ideal of or is a localization of a finitely generated -algebra.

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Additional Information

**Robert Gilmer**

Affiliation:
Department of Mathematics, Florida State University, Tallahassee, Florida 32306-3027

Email:
gilmer@math.fsu.edu

**William Heinzer**

Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395

Email:
heinzer@math.purdue.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-03847-1

Received by editor(s):
August 4, 1995

Received by editor(s) in revised form:
March 12, 1996

Communicated by:
Wolmer Vasconcelos

Article copyright:
© Copyright 1997
American Mathematical Society