Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Auslander, Modules over unramified regular local rings, Illinois J. Math. 5 (1961), 631–647.
M. Auslander and O. Goldman, Maximal orders, Trans. Amer. Math. Soc. 97 (1960), 1–24.
L. Avramov, Complete intersections and symmetric algebras, J. Algebra 73 (1980), 249–280.
J. Barshay, Graded algebras of powers of ideals generated by A-sequences, J. Algebra 25 (1973), 90–99.
D. Bayer and M. Stillman, Macaulay, A computer algebra system for computing in algebraic geometry and commutative algebra, 1988.
J. Brennan, M. Vaz Pinto and W. V. Vasconcelos, The Jacobian module of a Lie algebra, Trans. Amer. Math. Soc., to appear.
W. Bruns, Additions to the theory of algebras with straightening law, in Commutative Algebra (M. Hochster, C. Huneke and J.D. Sally, Eds.), MSRI Publications 15, Springer-Verlag, New York, 1989, 111–138.
D. Buchsbaum and D. Eisenbud, What makes a complex exact?, J. Algebra 25 (1973), 259–268.
D. Costa, L. Gallardo and J. Querré, On the distribution of prime elements in polynomial Krull domains, Proc. Amer. Math. Soc. 87 (1983), 41–43.
D.L. Costa and J.L. Johnson, Inert extensions for Krull domains, Proc. Amer. Math. Soc. 59 (1976), 189–194.
J. Eagon and D. G. Northcott, Ideals defined by matrices and a certain complex associated with them, Proc. Royal Soc. 269 (1962), 188–204.
E. G. Evans and P. Griffith, The syzygy problem, Annals of Math. 114 (1981), 323–333.
H. fitting, Die Determinantenideale Moduls, Jahresbericht DMV 46 (1936), 192–228.
O. Forster, Über die Anzahl der Erzeugenden eines Ideals in einem Noetherschen Ring, Math. Z. 84 (1964), 80–87.
F. R. Gantmacher, Applications of the Theory of Matrices, Interscience, New York, 1959.
M. Gerstenhaber, On dominance and varieties of commuting matrices, Annals of Math. 73 (1961), 324–348.
R. Gilmer, Multiplicative Ideal Theory, M. Dekker, New York, 1972.
J. Herzog, Certain complexes associated to a sequence and a matrix, Manuscripta Math. 12 (1974), 217–247.
J. Herzog, A. Simis and W. V. Vasconcelos, Approximation complexes of blowing-up rings, J. Algebra 74 (1982), 466–493.
J. Herzog, A. Simis and W. V. Vasconcelos, Koszul homology and blowing-up rings, Proc. Trento Commutative Algebra Conf., Lectures Notes in Pure and Applied Math., vol. 84, Dekker, New York, 1983, 79–169.
J. Herzog, A. Simis and W. V. Vasconcelos, On the arithmetic and homology of algebras of linear type, Trans. Amer. Math. Soc. 283 (1984), 661–683.
J. Herzog, A. Simis and W. V. Vasconcelos, Arithmetic of normal Rees algebras, Preprint, 1988.
J. Herzog, W. V. Vasconcelos and R. Villarreal, Ideals with sliding depth, Nagoya Math. J. 99 (1985), 159–172.
M. Hochster, The Zariski-Lipman conjecture in the graded case, J. Algebra 47 (1977), 411–424.
J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, Berlin, 1972.
C. Huneke, On the symmetric algebra of a module, J. Algebra 69 (1981), 113–119.
C. Huneke, Determinantal ideals of linear type, Arch. Math. 47 (1986), 324–329.
C. Huneke, On the symmetric and Rees algebras of an ideal generated by a d-sequence, J. Algebra 62 (1980), 268–275.
C. Huneke, Linkage and Koszul homology of ideals, Amer. J. Math. 104 (1982), 1043–1062.
C. Huneke, Strongly Cohen-Macaulay schemes and residual intersections, Trans. Amer. Math. Soc. 277 (1983), 739–763.
C. Huneke and M. E. Rossi, The dimension and components of symmetric algebras, J. Algebra 98 (1986), 200–210.
C. Huneke and B. Ulrich, Residual intersections, J. reine angew. Math. 390 (1988), 1–20.
T. Jòsefiak, Ideals generated by the minors of a symmetric matrix, Comment. Math. Helvetici 53 (1978), 595–607.
B. Kostant, Lie group representations on polynomial rings, Amer. J. Math. 85 (1963), 327–404.
B. V. Kotsev, Determinantal ideals of linear type of a generic symmetric matrix, J. Algebra, to appear.
L. Lebelt, Freie Auflösungen äußerer Potenzen, Manuscripta Math. 21 (1977), 341–355.
S. Lichtenbaum, On the vanishing of Tor in regular local rings, Illinois J. Math. 10 (1966), 220–226.
J. Lipman, Free derivation modules on algebraic varieties, American J. Math. 87 (1965), 874–898.
R. MacRae, On an application of the Fitting invariants, J. Algebra 2 (1965), 153–169.
H. Matsumura, Commutative Algebra, Benjamin/Cummings, Reading, Massachusetts, 1980.
A. Micali, Sur les algèbres universalles, Annales Inst. Fourier 14 (1964), 33–88.
A. Micali, P. Salmon and P. Samuel, Integrité et factorialité des algèbres symétriques, Atas do IV Colóquio Brasileiro de Matemática, SBM, (1965), 61–76.
T. Motzkin and O. Taussky, Pairs of matrices with property L II, Trans. Amer. Math. Soc. 80 (1955), 387–401.
M. Nagata, Local Rings, Interscience, New York, 1962.
R. W. Richardson, Commuting varieties of semisimple Lie algebras and algebraic groups, Compositio Math. 38 (1979), 311–327.
P. Roberts, A prime ideal in a polynomial ring whose symbolic blow-up is not Noetherian, Proc. Amer. Math. Soc. 94 (1985), 589–592.
P. Roberts, An infinitely generated symbolic blow-up in a power series ring and a new counterexample to Hilbert's Fourteenth Problem, J. Algebra, to appear.
P. Samuel, Anneaux gradués factoriels et modules réflexifs, Bull. Soc. Math. France 92 (1964), 237–249.
A. Simis, Selected Topics in Commutative Algebra, Lecture Notes, IX Escuela Latinoamericana de Matematica, Santiago, Chile, 1988.
A. Simis and W. V. Vasconcelos, The syzygies of the conormal module, Amer. J. Math. 103 (1981), 203–224.
A. Simis and W. V. Vasconcelos, On the dimension and integrality of symmetric algebras, Math. Z. 177 (1981), 341–358.
A. Simis and W. V. Vasconcelos, The Krull dimension and integrality of symmetric algebras, Manuscripta Math. 61 (1988), 63–78.
G. Valla, On the symmetric and Rees algebras of an ideal, Manuscripta Math. 30 (1980), 239–255.
W. V. Vasconcelos, On linear complete intersections, J. Algebra 111 (1987), 306–315.
W. V. Vasconcelos, Symmetric algebras and factoriality, in Commutative Algebra (M. Hochster, C. Huneke and J. D. Sally, Eds.), MSRI Publications 15, Springer-Verlag, New York, 1989, 467–496.
W. V. Vasconcelos, The complete intersection locus of certain ideals, J. Pure and Applied Algebra 38 (1985), 367–378.
W. V. Vasconcelos, On the structure of certain ideal transforms, Math. Z. 198 (1988), 435–448.
W. V. Vasconcelos, Modules of differentials of symmetric algebras, Arch. Math., to appear.
U. Vetter, Zu einem Satz von G. Trautmann über den Rang gewisser kohärenter analytischer Moduln, Arch. Math. 24 (1973), 158–161.
R. Villarreal, Rees algebras and Koszul homology, J. Algebra 119 (1988), 83–104.
R. Villarreal, Cohen-Macaulay graphs, Preprint, 1988.
J. Weyman, Resolutions of the exterior and symmetric powers of a module, J. Algebra 58 (1979), 333–341.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag
About this paper
Cite this paper
Vasconcelos, W.V. (1990). Symmetric algebras. In: Bruns, W., Simis, A. (eds) Commutative Algebra. Lecture Notes in Mathematics, vol 1430. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085540
Download citation
DOI: https://doi.org/10.1007/BFb0085540
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52745-9
Online ISBN: 978-3-540-47136-3
eBook Packages: Springer Book Archive