Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Mobile Device Pairing
 Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

On the homology of associative algebras

Author(s): David J. Anick
Journal: Trans. Amer. Math. Soc. 296 (1986), 641-659.
MSC: Primary 16A62; Secondary 13D03, 55S10
MathSciNet review: 846601
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We present a new free resolution for $ k$ as an $ G$-module, where $ G$ is an associative augmented algebra over a field $ k$. The resolution reflects the combinatorial properties of $ G$.

References:

[1]
D. Anick, Non-commutative graded algebras and their Hilbert series, J. Algebra 78 (1982), 120-140. MR 677714 (84g:16001)

[2]
D. Anick and C. Löfwall, Hilbert series of finitely presented algebras, Algebra, Algebraic Topology, and their Interactions, Lecture Notes in Math., vol. 1183, Springer-Verlag, pp. 32-55. MR 846437 (87k:16002)

[3]
J. Backelin, La série de Poincaré-Betti d'une algèbre graduée de type fini à une relation est rationnelle, C. R. Acad. Sci. Paris. Sér. A 287 (1978), 843-846. MR 551760 (81f:16002)

[4]
-, Les anneaux locaux á relations monomiales ont des séries de Poincaré-Betti rationnelles, C. R. Acad. Sci. Paris Sér. I 295 (1982), 607-610. MR 686351 (85a:13008)

[5]
J. Backelin and R. Fröberg, Koszul algebras, Veronese subrings, and rings with linear resolutions, Rev. Roumaine Math. Pures Appl. 30 (1985), 85-97. MR 789425 (87c:16002)

[6]
G. Bergman, The diamond lemma for ring theory, Adv. in Math. 29 (1978), 178-218. MR 506890 (81b:16001)

[7]
D. B. A. Epstein and N. E. Steenrod, Cohomology operations, Ann. of Math. Studies, No. 50, Princeton Univ. Press, Princeton, N.J., 1962. MR 0145525 (26:3056)

[8]
V. E. Govorov, Graded algebras, Math. Notes 12 (1972), 552-556. MR 0318199 (47:6746)

[9]
-, Dimension and multiplicity of graded algebras, Siberian Math. J. 14 (1973), 1200-1206. MR 0340342 (49:5097)

[10]
D. Lazard, Algèbre linéaire sur $ k[{x_1}, \ldots ,{x_n}]$ et élimination, Bull. Soc. Math. France 105 (1977), 165-190. MR 0491702 (58:10905)

[11]
F. S. Macaulay, Some properties of enumeration in the theory of modular systems, Proc. London Math. Soc. 26 (1927), 531-555.

[12]
S. Priddy, Koszul resolutions, Trans. Amer. Math. Soc. 152 (1970), 39-77. MR 0265437 (42:346)

[13]
G. Sjödin, A set of generators for $ \operatorname{Ext}_R(k,k)$, Math. Scand. 38 (1976), 199-210. MR 0422248 (54:10239)

[14]
R. P. Stanley, Hilbert functions of graded algebras, Adv. in Math. 28 (1978), 57-83. MR 0485835 (58:5637)

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC: 16A62, 13D03, 55S10

Retrieve articles in all Journals with MSC: 16A62, 13D03, 55S10

Additional Information:

DOI: 10.1090/S0002-9947-1986-0846601-5
PII: S0002-9947-1986-0846601-5
Copyright of article: Copyright 1986, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia