Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-30T21:15:45.808Z Has data issue: false hasContentIssue false

A Cohen–Macaulay algebra has only finitely many semidualizing modules

Published online by Cambridge University Press:  01 November 2008

LARS WINTHER CHRISTENSEN
Affiliation:
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, U.S.A. e-mail: [email protected]
SEAN SATHER-WAGSTAFF
Affiliation:
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, U.S.A. e-mail: [email protected]

Abstract

We prove the result stated in the title, which answers the equicharacteristic case of a question of Vasconcelos.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Cartan, H. and Eilenberg, S. Homological algebra, Princeton Landmarks in Mathematics (Princeton University Press, 1999), With an appendix by D. A. Buchsbaum. Reprint of the 1956 original. MR 1731415Google Scholar
[2]Christensen, L. W.Semi-dualizing complexes and their Auslander categories. Trans. Amer. Math. Soc. 353 (2001), no. 5, 18391883. MR 1813596CrossRefGoogle Scholar
[3]Frankild, A. and Sather–Wagstaff, S.Reflexivity and ring homomorphisms of finite flat dimension. Comm. Algebra 35 (2007), no. 2, 461500. MR 2294611CrossRefGoogle Scholar
[4]Frankild, A. and Sather–Wagstaff, S.The set of semidualizing complexes is a nontrivial metric space. J. Algebra 308 (2007), no. 1, 124143. MR 2290914CrossRefGoogle Scholar
[5]Grothendieck, A.Éléments de géométrie algébrique III. Étude cohomologique des faisceaux cohérents I. Inst. Hautes Études Sci. Publ. Math. (1961), no. 11, 167. MR 0163910Google Scholar
[6]Happel, D.Selforthogonal Modules, Abelian groups and modules (Padova, 1994), Math. Appl., vol. 343 (Kluwer Acad. Publ., 1995), pp. 257276. MR 1378204Google Scholar
[7]Sather–Wagstaff, S.Semidualizing modules and the divisor class group. Illinois J. Math. 51 (2007), no. 1, 255285. MR 2346197CrossRefGoogle Scholar
[8]Vasconcelos, W. V. Divisor Theory in Module Categories (North-Holland Publishing Co., 1974). North-Holland Mathematics Studies, No. 14, Notas de Matemática No. 53. [Notes on Mathematics, No. 53]. MR 0498530Google Scholar