Illinois Journal of Mathematics

Equidimensional symmetric algebras and residual intersections

Mark R. Johnson

Full-text: Open access

Abstract

For a finitely generated module $M$, over a universally catenary local ring, whose symmetric algebra is equidimensional, the ideals generated by the rows of a minimal presentation matrix are shown to have height at most $\mu(M) - \rank M$. Moreover, in the extremal case, they are Cohen-Macaulay ideals if the symmetric algebra is Cohen-Macaulay. Some applications are given to residual intersections of ideals.

Article information

Source
Illinois J. Math., Volume 45, Number 1 (2001), 187-193.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138262

Digital Object Identifier
doi:10.1215/ijm/1258138262

Mathematical Reviews number (MathSciNet)
MR1849993

Zentralblatt MATH identifier
0999.13006

Subjects
Primary: 13C15: Dimension theory, depth, related rings (catenary, etc.)
Secondary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]

Citation

Johnson, Mark R. Equidimensional symmetric algebras and residual intersections. Illinois J. Math. 45 (2001), no. 1, 187--193. doi:10.1215/ijm/1258138262. https://projecteuclid.org/euclid.ijm/1258138262


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