Journal of Commutative Algebra

Short Koszul modules

Luchezar L. Avramov, Srikanth B. Iyengar, and Liana M. Şega

Full-text: Open access

Article information

Source
J. Commut. Algebra, Volume 2, Number 3 (2010), 249-279.

Dates
First available in Project Euclid: 18 October 2010

Permanent link to this document
https://projecteuclid.org/euclid.jca/1287409177

Digital Object Identifier
doi:10.1216/JCA-2010-2-3-249

Mathematical Reviews number (MathSciNet)
MR2728144

Zentralblatt MATH identifier
1237.13025

Subjects
Primary: 13D02: Syzygies, resolutions, complexes
Secondary: 13A02: Graded rings [See also 16W50] 13D07: Homological functors on modules (Tor, Ext, etc.)

Keywords
Koszul algebras Koszul module

Citation

Avramov, Luchezar L.; Iyengar, Srikanth B.; Şega, Liana M. Short Koszul modules. J. Commut. Algebra 2 (2010), no. 3, 249--279. doi:10.1216/JCA-2010-2-3-249. https://projecteuclid.org/euclid.jca/1287409177


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References

  • L.L. Avramov, Infinite free resolutions, Six lectures on commutative algebra (Bellaterra, 1996), Progr. Math. 166, Birkhäuser, Basel, 1998%; pp. 1–118.
  • L.L. Avramov, S.B. Iyengar and L.M. Şega, Free resolutions over short local rings, J. London Math. Soc. 78 (2008), 459-476.
  • J. Backelin and R. Fröberg, Koszul algebras, Veronese subrings and rings with linear resolutions, Rev. Roum. Math. Pures Appl. 30 (1985), 85-97.
  • D.A. Buchsbaum and D. Eisenbud, Algebra structures for finite free resolutions, and some structure theorems for ideals of codimension $3$, Amer. J. Math. 99 (1977), 447-485.
  • A. Conca, Gröbner bases for spaces of quadrics of low codimension, Adv. Appl. Math. 24 (2000), 111-124.
  • A. Conca, M.-E. Rossi and G. Valla, Gröbner flags and Gorenstein algebras, Compos. Math. 129 (2000), 95-121.
  • A. Conca, N.V. Trung and G. Valla, Koszul property for points in projective spaces, Math. Scand. 89 (2001), 201-216.
  • D. Eisenbud, Homological algebra on a complete intersection, with an application to group representations, Trans. Amer. Math. Soc. 260 (1980), 35-64.
  • R. Fröberg, Koszul algebras, Advances in commutative ring theory (Fez, 1997), %337–350, Lecture Notes Pure Appl. Math. 205, Dekker, New York, 1999.
  • R. Fröberg and C. Löfwall, Koszul homology and Lie algebras with application to generic forms and points, Homology, Homotopy, Appl. 4 (2002), 227-258.
  • V.N. Gasharov and I.V. Peeva, Boundedness versus periodicity over commutative local rings, Trans. Amer. Math. Soc. 320 (1990), 569-580.
  • A. Grothendieck and J. Dieudonné, Éléments de géometrie algébrique, IV. Étude locale des schémas et des morphismes de schémas (Seconde partie), Publ. Math. IHES 24, 1965.
  • ––––, Éléments de géometrie algébrique, IV. Étude locale des schémas et des morphismes de schémas (Troisième partie), Publ. Math. IHES 28, 1966.
  • T.H. Gulliksen, Massey operations and the Poincaré series of certain local rings, J. Algebra 22 (1972), 223-232.
  • D.A. Jorgensen and L.M. Şega, Nonvanishing cohomology and classes of Gorenstein rings, Adv. Math. 188 (2004), 470-490.
  • ––––, Independence of the total reflexivity conditions for modules, Algeb. Represent. Theory 9 (2006), 217-226.
  • J. Lescot, Asymptotic properties of Betti numbers of modules over certain rings, J. Pure Appl. Algebra 38 (1985), 287-298.
  • C. Löfwall, On the subalgebra generated by the one-dimensional elements in the Yoneda Ext-algebra, Algebra, algebraic topology and their interactions (Stockholm, 1983), Lecture Notes Math. 1183, Springer, Berlin, 1986%; pp. 291–338.
  • A. Polishchuk and L. Positselski, Quadratic algebras, Univ. Lecture Ser. 37, American Mathematical Society, Providence, RI, 2005.
  • J.-E. Roos, Relations between Poincaré-Betti series of loop spaces and of local rings, Sém. Algèbr. Paul Dubreil 31ème année (Paris, 1977-1978), Lecture Notes Math. 740, Springer, Berlin, 1979%; pp. 285–322.