On the generalized Nakayama conjecture and the Cartan determinant problem-Reference-Cited by-同舟云学术

On the generalized Nakayama conjecture and the Cartan determinant problem

Published:1986 Issue:2 Volume:294 Page:679-691
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Fuller K. R.,Zimmermann-Huisgen B.

Abstract

For Artin algebras allowing certain filtered module categories, the Generalized Nakayama Conjecture is shown to be true; our result covers all positively graded Artin algebras and those whose radical cube is zero. For the corresponding class of left artinian rings we prove that finite global dimension forces the determinant of the Cartan matrix to be 1.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1986-294-02/S0002-9947-1986-0825739-2/S0002-9947-1986-0825739-2.pdf

Reference11 articles.

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3. On graded rings with finiteness conditions;Camillo, V. P.;Proc. Amer. Math. Soc.,1982

4. Algebras of cohomologically finite dimension;Eilenberg, Samuel;Comment. Math. Helv.,1954

5. Graded Artin algebras;Gordon, Robert;J. Algebra,1982

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