Some dimension cases of the canonical element conjecture

Authors:
Craig Huneke and Jee Koh

Journal:
Proc. Amer. Math. Soc. **98** (1986), 394-398

MSC:
Primary 13H10; Secondary 13D25

DOI:
https://doi.org/10.1090/S0002-9939-1986-0857928-0

MathSciNet review:
857928

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Abstract | References | Similar Articles | Additional Information

Abstract: The Canonical Element Conjecture holds for those -dimensional local rings of depth 2 whose second local cohomology module is a finite direct sum of cyclic modules, and for those -dimensional local rings whose second local cohomology module is cyclic.

**[1]**M. Brodmann,*Finiteness of ideal transforms*, J. Algebra**63**(1980), 162-185. MR**568570 (81g:13004)****[2]**W. Bruns,*The Eisenbud-Evans principal ideal theorem and determinantal ideals*, Proc. Amer. Math. Soc.**83**(1981), 19-24. MR**619972 (82k:13010)****[3]**D. Eisenbud and E. G. Evans, Jr.,*A generalized principal ideal theorem*, Nagoya Math. J.**62**(1976), 41-53. MR**0409440 (53:13195)****[4]**A. Grothendieck (notes by R. Hartshorne),*Local cohomology*, Lecture Notes in Math., vol. 41, Springer-Verlag, 1967. MR**0224620 (37:219)****[5]**M. Hochster,*Topics in the homological theory of modules over commutative rings*, CBMS Regional Conf. Ser. in Math., no. 24, Amer. Math. Soc., Providence, R. I., 1975. MR**0371879 (51:8096)****[6]**-,*Canonical elements in local cohomology modules and the direct summand conjecture*, J. Algebra**84**(1983), 503-553. MR**723406 (85j:13021)****[7]**J. Koh,*Degree**extensions of an unramified regular local ring of mixed characteristic*, J. Algebra (to appear).**[8]**P. Roberts,*The equivalence of two forms of the Canonical Element Conjecture*, preprint.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1986-0857928-0

Keywords:
Canonical Element Conjecture,
local cohomology

Article copyright:
© Copyright 1986
American Mathematical Society