On the symmetry of the finitistic dimension

Henning Krause

doi:10.5802/crmath.481

Representation theory

On the symmetry of the finitistic dimension

Henning Krause ¹

¹ Fakultät für Mathematik Universität Bielefeld D-33501 Bielefeld Germany

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1449-1453.

Abstract

For any ring we propose the construction of a cover which increases the finitistic dimension on one side and decreases the finitistic dimension to zero on the opposite side. This complements recent work of Cummings.

Received: 2022-11-20
Revised: 2023-01-25
Accepted: 2023-02-20
Published online: 2023-11-10

DOI: 10.5802/crmath.481

Classification: 16E10

Author's affiliations:

Henning Krause ¹

¹ Fakultät für Mathematik Universität Bielefeld D-33501 Bielefeld Germany

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {On the symmetry of the finitistic dimension},
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Henning Krause. On the symmetry of the finitistic dimension. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1449-1453. doi : 10.5802/crmath.481. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.481/

References
Cited by

[1] Maurice Auslander; David A. Buchsbaum Homological dimension in noetherian rings. II, Trans. Am. Math. Soc., Volume 88 (1958), pp. 194-206 | MR | Zbl

[2] Hyman Bass Finitistic dimension and a homological generalization of semi-primary rings, Trans. Am. Math. Soc., Volume 95 (1960), pp. 466-488 | DOI | MR | Zbl

[3] Charley Cummings Left-right symmetry of finite finitistic dimension (2022) | arXiv

[4] Ellen Kirkman; James Kuzmanovich Algebras with large homological dimensions, Proc. Amer. Math. Soc., Volume 109 (1990) no. 4, pp. 903-906 | DOI | MR | Zbl

[5] Henning Krause Homological theory of representations, Cambridge Studies in Advanced Mathematics, 195, Cambridge University Press, 2022 | Zbl

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