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Open Access. Powered by Scholars. Published by Universities.®

Mathematics

2003

Syracuse University

Articles 1 - 6 of 6

Full-Text Articles in Physical Sciences and Mathematics

On A Conjecture Of Auslander And Reiten, Craig Huneke, Graham J. Leuschke Apr 2003

On A Conjecture Of Auslander And Reiten, Craig Huneke, Graham J. Leuschke

Mathematics - All Scholarship

In studying Nakayama's 1958 conjecture on rings of infinite dominant dimension, Auslander and Reiten proposed the following generalization: Let Lambda be an Artin algebra and M a Lambda-generator such that ExtiLambda(M,M)=0 for all i \geq 1; then M is projective. This conjecture makes sense for any ring. We establish Auslander and Reiten's conjecture for excellent Cohen-Macaulay normal domains containing the rational numbers, and slightly more generally.

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Local Rings Of Bounded Cohen-Macaulay Type, Graham J. Leuschke, Roger Wiegand Apr 2003

Local Rings Of Bounded Cohen-Macaulay Type, Graham J. Leuschke, Roger Wiegand

Mathematics - All Scholarship

Let (R,m,k) be a local Cohen-Macaulay (CM) ring of dimension one. It is known that R has finite CM type if and only if R is reduced and has bounded CM type. Here we study the one-dimensional rings of bounded but infinite CM type. We will classify these rings up to analytic isomorphism (under the additional hypothesis that the ring contains an infinite field). In the first section we deal with the complete case, and in the second we show that bounded CM type ascends to and descends from the completion. In the third section we study ascent and descent …

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Hypersurfaces Of Bounded Cohen-Macaulay Type, Graham J. Leuschke, Roger Wiegand Apr 2003

Hypersurfaces Of Bounded Cohen-Macaulay Type, Graham J. Leuschke, Roger Wiegand

Mathematics - All Scholarship

Let R = k[[x0, . . . , xd]]/(f), where k is a field and f is a non-zero non-unit of the formal power series ring k[[x0, . . . , xd]]. We investigate the question of which rings of this form have bounded Cohen–Macaulay type, that is, have a bound on the multiplicities of the indecomposable maximal Cohen–Macaulaymodules. As with finite Cohen–Macaulay type, if the characteristic is different from two, the question reduces to the one-dimensional case: The ring R has bounded Cohen–Macaulay type if and only if R ∼= k …

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Local Spectra Of Operator Weighted Shifts, Abdellatif Bourhim Apr 2003

Local Spectra Of Operator Weighted Shifts, Abdellatif Bourhim

Mathematics - All Scholarship

In this paper, we study the local spectral properties of unilateral operator weighted shifts.

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On The Local Spectral Properties Of Weighted Shift Operators, Abdellatif Bourhim Mar 2003

On The Local Spectral Properties Of Weighted Shift Operators, Abdellatif Bourhim

Mathematics - All Scholarship

In this paper, we study the local spectral properties for both unilateral and bilateral weighted shift operators.

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Khovanov Homology And Conway Mutation, Stephan Wehrli Jan 2003

Khovanov Homology And Conway Mutation, Stephan Wehrli

Mathematics - All Scholarship

We present an easy example of mutant links with different Khovanov homology. The existence of such an example is important because it shows that Khovanov homology cannot be defined with a skein rule similar to the skein relation for the Jones polynomial.

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