On the depth of the symmetric algebra
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- by J. Herzog, M. E. Rossi and G. Valla
- Trans. Amer. Math. Soc. 296 (1986), 577-606
- DOI: https://doi.org/10.1090/S0002-9947-1986-0846598-8
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Abstract:
Let $(R,\mathfrak {m})$ be a local ring. Assume that $R = A/I$, where $(A,\mathfrak {n})$ is a regular local ring and $I \subseteq {\mathfrak {n}^2}$ is an ideal. The depth of the symmetric algebra $S(\mathfrak {m})$ of $\mathfrak {m}$ over $R$ is computed in terms of the depth of the associated graded module ${\text {gr}_\mathfrak {n}}(I)$ and the so-called "strong socle condition." Explicit results are obtained, for instance, if $I$ is generated by a super-regular sequence, if $I$ has a linear resolution or if $I$ has projective dimension one.References
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Bibliographic Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 296 (1986), 577-606
- MSC: Primary 13C15; Secondary 13H10
- DOI: https://doi.org/10.1090/S0002-9947-1986-0846598-8
- MathSciNet review: 846598