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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 1389520
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $(R, \mathbf {m})$ be a local (Noetherian) ring. The main result of this paper asserts the existence of a local extension ring $S$ of $R$ such that (i) $S$ dominates $R$, (ii) the residue field of $S$ is a finite purely transcendental extension of $R/ \mathbf {m}$, (iii) every associated prime of (0) in $S$ contracts in $R$ to an associated prime of (0), and (iv) $\dim (S) \le 1$. In addition, it is shown that $S$ can be obtained so that either $ \mathbf {m} S$ is the maximal ideal of $S$ or $S$ is a localization of a finitely generated $R$-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: http://dx.doi.org/10.1090/S0002-9939-97-03847-1
PII: S 0002-9939(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