Abstract
The aim of this paper is to prove that many homological properties and estimates of the discrete straightening ring still remain valid for the straightening ring itself. E.g. Cohen-Macaulay property, generalised Cohen-Macaulay property and Serre condition (Sn) (the latter for unmixed discrete straightening rings) transfer. The main technical tool is a further development of a spectral sequence argument well known in the case of associated graded rings.
Similar content being viewed by others
5. Literatur
M. Aigner: Combinatorial theory. Springer, Berlin, 1979.
M. Auslander, D. Bridger: Stable module theory. Memoirs of the Amer.Math.Soc. 94 (1969).
K. Baclawski: Rings with lexicographic straightening law. Adv. Math. 39 (1981), 185–213.
D.A. Bayer: The division algorithm and the Hilbert scheme. Thesis, Harvard Univ., 1982.
W. Bruns, U. Vetter: Determinantal rings. Lecture notes in mathematics 1327, Springer, Berlin, 1983.
B. Buchberger: Gröbner bases: An algorithmic method in polynomial ideal theory. In: Recent trends in multi-dimensiona1 system theory (N.K. Bose ed.), Reidel, Dortrecht, 1985, 184–232.
H.Cartan, S.Eilenberg: Homological algebra. Princeton, 1956.
C. DeConcini, D. Eisenbud,C. Procesi: Hodge algebras. Asterisque 91 (1982).
L.E. Dickson: Amer. J. Math. 35 (1913), 413–426.
A. Dress, G. Schiffeis: Noetherian quasiorders and canonical ideal bases. Manuskript, Bielefeld 1988.
H. Flenner: Rationale quasihomogene Singularitäten. Archiv Math. 36 (1981), 35–44.
S. Goto, K. Watanabe: On graded rings II. Tokyo J. Math. 1 (1978), 237–261.
H.-G. Gräbe: The canonical module of a Stanley-Reisner ring. J. Alg. 86 (1984), 272–281.
H.-G. Gräbe: Über Streckungsringe. Beitr. Alg. Geom. 23 (1986), 85–100.
H.-G. Gräbe: Resolving algebras with straightening law. Eingereicht bei J. Alg.
H.-G. Gräbe: Der Stanley-Reisner-Ring eines simplizialen Komplexes. Dissertation A, Halle/S. 1982.
H.-G. Gräbe: Homologien von Streckungsringen. Erscheint in WZ der PH Erfurt.
H.-G. Gräbe: Streckungsringe. Dissertation B, Erfurt 1988.
H.-M. Möller, F. Mora: New constructive methods in classical ideal theory. J. Alg. 100 (1986), 138–178.
F. Mora, L.Robbiano: The Gröbner fan of an ideal. Preprint, Univ. of Genova, 1337.
P. Schensel: Dualisierende Komplexe in der lokalen Algebra und Buchsbaumringe. Lecture Notes in Math. 907 (1982).
G. Sjödin: On filtered modules and their associated graded modules. Math. Scand. 33 (1973), 229–249.
F. Winkler, B. Buchberger, F. Lichtenberger, H. Rolletschek; An algorithm for constructing canonical bases of polynomial ideals. ACM Trans.Math.Software 11 (1985), 66–73.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gräbe, HG. Moduln über Streckungsringen. Results. Math. 15, 202–220 (1989). https://doi.org/10.1007/BF03322612
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03322612