Abstract
We give some necessary and sufficient conditions for SA(m) being Cohen-Macaulay, where SA(m) is the Symmetric algebra of the maximal ideal of an homomorphic image A of a regular local ring.
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EAGON,J.A., NORTHCOTT,D.G.: Ideals defined by matrices and a certain complex associated with them. Proc. Royal Soc. A269, 188–204 (1962)
KAPLANSKY,I.: Commutative Rings. The University of Chicago Press.1974
MICALI,A.: Sur les algebres universelles (Thesis). Ann. Inst. Fourier Grenoble.14, 33–88 (1964)
REES,D.: A note on form rings and ideals. Mathematika4, 51–60 (1957)
ROBBIANO,L., VALLA,G.: Teoria della piattezza normale: alcuni aspetti e problemi. Seminario dell' Istituto di Matematica di Genova,8 (1978)
ROSSI,M.E.: Sulle algebre di Rees e Simmetrica di un ideale (to appear)
SALLY,J.: Number of generators of ideals in local rings. Dekker. New York and Basel 1978
VALABREGA,P., VALLA,G.: Form rings and regular sequences. Nagoya Math. J.72, 93–101 (1978)
VALLA,G.: Certain graded algebras are always Cohen-Macaulay. J. of Algebra42, 537–548 (1976)
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This paper was supported by C.N.R. (Consiglio Nazionale delle Ricerche)
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Rossi, M.E. On symmetric algebras which are Cohen Macaulay. Manuscripta Math 34, 199–210 (1981). https://doi.org/10.1007/BF01165536
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DOI: https://doi.org/10.1007/BF01165536