Generic Gaussian ideals

Alberto Corso; Wolmer V. Vasconcelos; Rafael H. Villarreal

doi:10.1016/S0022-4049(97)80001-1

Generic Gaussian ideals

Alberto Corso, Wolmer V. Vasconcelos, Rafael H. Villarreal

Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

The content of a polynomial f(t) is the ideal generated by its coefficients. Our aim here is to consider a beautiful formula of Dedekind-Mertens on the content of the product of two polynomials, to explain some of its features from the point of view of Cohen-Macaulay algebras and to apply it to obtain some Noether normalizations of certain toric rings. Furthermore, the structure of the primary decomposition of generic products is given and some extensions to joins of toric rings are considered.

Original language	English
Pages (from-to)	117-127
Number of pages	11
Journal	Journal of Pure and Applied Algebra
Volume	125
Issue number	1-3
DOIs	https://doi.org/10.1016/S0022-4049(97)80001-1
State	Published - Mar 1998

Bibliographical note

Funding Information:
A. Corso gratefully acknowledgesp artial support from the Consiglio Nazionale delle Ricerche under CNR grant 203.01.63.W . V. Vasconcelos was in part supportedb y a NSF grant. Finally, R. H. Villarreal expressesh is gratitudet o COFAA-IPN, CONACyT, and SNI.

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/S0022-4049(97)80001-1

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abstract = "The content of a polynomial f(t) is the ideal generated by its coefficients. Our aim here is to consider a beautiful formula of Dedekind-Mertens on the content of the product of two polynomials, to explain some of its features from the point of view of Cohen-Macaulay algebras and to apply it to obtain some Noether normalizations of certain toric rings. Furthermore, the structure of the primary decomposition of generic products is given and some extensions to joins of toric rings are considered.",

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note = "Funding Information: A. Corso gratefully acknowledgesp artial support from the Consiglio Nazionale delle Ricerche under CNR grant 203.01.63.W . V. Vasconcelos was in part supportedb y a NSF grant. Finally, R. H. Villarreal expressesh is gratitudet o COFAA-IPN, CONACyT, and SNI.",

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AU - Corso, Alberto

AU - Vasconcelos, Wolmer V.

AU - Villarreal, Rafael H.

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PY - 1998/3

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N2 - The content of a polynomial f(t) is the ideal generated by its coefficients. Our aim here is to consider a beautiful formula of Dedekind-Mertens on the content of the product of two polynomials, to explain some of its features from the point of view of Cohen-Macaulay algebras and to apply it to obtain some Noether normalizations of certain toric rings. Furthermore, the structure of the primary decomposition of generic products is given and some extensions to joins of toric rings are considered.

AB - The content of a polynomial f(t) is the ideal generated by its coefficients. Our aim here is to consider a beautiful formula of Dedekind-Mertens on the content of the product of two polynomials, to explain some of its features from the point of view of Cohen-Macaulay algebras and to apply it to obtain some Noether normalizations of certain toric rings. Furthermore, the structure of the primary decomposition of generic products is given and some extensions to joins of toric rings are considered.

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DO - 10.1016/S0022-4049(97)80001-1

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EP - 127

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 1-3

ER -

Generic Gaussian ideals

Abstract

Bibliographical note

ASJC Scopus subject areas

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