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Free Lie subalgebras of the cohomology of local rings. (English) Zbl 0516.13022


MSC:

13H15 Multiplicity theory and related topics
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
13D99 Homological methods in commutative ring theory
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
13C10 Projective and free modules and ideals in commutative rings
18G99 Homological algebra in category theory, derived categories and functors
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[1] M. André, Hopf algebras with divided powers, J. Algebra 18 (1971), 19 – 50. · Zbl 0217.07102
[2] L. L. Avramov, The Hopf algebra of a local ring, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 253 – 277 (Russian). · Zbl 0295.13005
[3] Luchezar L. Avramov, Small homomorphisms of local rings, J. Algebra 50 (1978), no. 2, 400 – 453. · Zbl 0395.13005
[4] Luchezar L. Avramov, Poincaré series of almost complete intersections of embedding dimension three, PLISKA Stud. Math. Bulgar. 2 (1981), 167 – 172. · Zbl 0516.13021
[5] -, Sur la croissance des nombres de Betti d’un anneau local, C. R. Acad. Sci. Paris, Ser. A-B 289 (1979), A369-A372.
[6] L. L. Avramov and E. S. Golod, The homology of algebra of the Koszul complex of a local Gorenstein ring, Mat. Zametki 9 (1971), 53 – 58 (Russian). · Zbl 0213.04904
[7] Walter Borho and Hanspeter Kraft, Über die Gelfand-Kirillov-Dimension, Math. Ann. 220 (1976), no. 1, 1 – 24. · Zbl 0306.17005
[8] Kuo-tsai Chen, Free subalgebras of loop space homology and Massey products, Topology 11 (1972), 237 – 243. · Zbl 0238.55006
[9] Allan Clark, Homotopy commutativity and the Moore spectral sequence, Pacific J. Math. 15 (1965), 65 – 74. · Zbl 0129.38805
[10] E. S. Golod, Homologies of some local rings, Dokl. Akad. Nauk SSSR 144 (1962), 479 – 482 (Russian).
[11] E. S. Golod, Homology of some local rings, Uspekhi Mat. Nauk 33 (1978), no. 5(203), 177 – 178 (Russian). · Zbl 0417.13010
[12] V. K. A. M. Gugenheim and J. Peter May, On the theory and applications of differential torsion products, American Mathematical Society, Providence, R.I., 1974. Memoirs of the American Mathematical Society, No. 142. · Zbl 0292.55019
[13] T. H. Gulliksen, On the deviations of a local ring, Math. Scand. 47 (1980), no. 1, 5 – 20. · Zbl 0458.13010
[14] Tor H. Gulliksen and Gerson Levin, Homology of local rings, Queen’s Paper in Pure and Applied Mathematics, No. 20, Queen’s University, Kingston, Ont., 1969. · Zbl 0208.30304
[15] Christer Lech, Inequalities related to certain couples of local rings, Acta Math. 112 (1964), 69 – 89. · Zbl 0123.03602
[16] J. Peter May, Matric Massey products, J. Algebra 12 (1969), 533 – 568. · Zbl 0192.34302
[17] Günter Scheja, Über die Bettizahlen lokaler Ringe, Math. Ann. 155 (1964), 155 – 172 (German). · Zbl 0134.27203
[18] Gunnar Sjödin, Hopf algebras and derivations, J. Algebra 64 (1980), no. 1, 218 – 229. · Zbl 0429.16008
[19] Jack Shamash, The Poincaré series of a local ring, J. Algebra 12 (1969), 453 – 470. · Zbl 0189.04004
[20] Hartmut Wiebe, Über homologische Invarianten lokaler Ringe, Math. Ann. 179 (1969), 257 – 274 (German). · Zbl 0169.05701
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