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Certain graded algebras are always Cohen-Macaulay. (English) Zbl 0338.13013


MSC:

13C15 Dimension theory, depth, related commutative rings (catenary, etc.)
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
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References:

[1] Barshay, J., Graded algebras of powers of ideal generated by \(A\)-sequences, J. Algebra, 25, 90-99 (1973) · Zbl 0256.13017
[2] Barshay, J., Determinantal varieties, monomial semigroups, and algebras associated with ideals, (Proc. Amer. Math. Soc., 40 (1973)), 16-22 · Zbl 0273.14021
[3] Caruth, A., On powers of ideals generated by \(R\)-sequences in a Noetherian local ring, (Proc. Cambridge Philos. Soc., 74 (1973)), 441-444 · Zbl 0267.13001
[4] Hochster, M.; Eagon, J. A., A class of perfect determinantals ideals, Bull. Amer. Math. Soc., 76, 1026-1029 (1970) · Zbl 0201.37201
[5] Hochster, M.; Ratliff, L. J., Five theorems on Macaulay rings, Pacific J. Math., 44, 147-172 (1973) · Zbl 0239.13016
[6] Micali, A., Sur les algèbres universelles, Ann. Inst. Fourier (Grenoble), 14, 33-38 (1964) · Zbl 0152.02602
[7] Ratliff, L. J., Two notes on locally Macaulay rings, Trans. Amer. Math. Soc., 119, 399-406 (1965) · Zbl 0133.29201
[8] Ratliff, L. J., On quasy unmidex local domains, the altitude formula, and the chain condition for prime ideals (II), Amer. J. Math., 92, 99-144 (1970) · Zbl 0198.06003
[9] Rees, D., A note on form rings and ideals, Mathematika, 4, 51-60 (1957) · Zbl 0089.26003
[10] Sakaguchi, M., A note on graded Gorenstein Modules, Hiroshima Math. J., 4, 339-341 (1974) · Zbl 0298.13013
[11] Zariski, O.; Samuel, P., (Commutative Algebra, Vol. II (1960), Van Nostrand: Van Nostrand Princeton, N.J.) · Zbl 0112.02902
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