Koszul modules (and the Omega-growth of modules) over short local algebras

Ringel CM, Zhang P (2021)
Journal of Pure and Applied Algebra 225(12): 106772.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Following the well-established terminology in commutative algebra, any (not necessarily commutative) finite-dimensional local algebra A with radical Jwill be said to be shortprovided J(3)= 0. As in the commutative case, also in general, the asymptotic behavior of the Betti numbers of modules seems to be of interest. As we will see, there are only few possibilities for the growth of the Betti numbers of modules. And there is a class of modules, the Koszul modules, where the Betti numbers can be calculated quite easily. We generalize results which are known for commutative algebras, but some of our results seem to be new also in the commutative case. (c) 2021 Elsevier B.V. All rights reserved.
Stichworte
Short local algebra; Betti number; Omega-growth; Koszul module; Left; Koszul algebra; Left Conca ideal
Erscheinungsjahr
2021
Zeitschriftentitel
Journal of Pure and Applied Algebra
Band
225
Ausgabe
12
Art.-Nr.
106772
ISSN
0022-4049
eISSN
1873-1376
Page URI
https://pub.uni-bielefeld.de/record/2956283

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Ringel CM, Zhang P. Koszul modules (and the Omega-growth of modules) over short local algebras. Journal of Pure and Applied Algebra. 2021;225(12): 106772.
Ringel, C. M., & Zhang, P. (2021). Koszul modules (and the Omega-growth of modules) over short local algebras. Journal of Pure and Applied Algebra, 225(12), 106772. https://doi.org/10.1016/j.jpaa.2021.106772
Ringel, C. M., and Zhang, P. (2021). Koszul modules (and the Omega-growth of modules) over short local algebras. Journal of Pure and Applied Algebra 225:106772.
Ringel, C.M., & Zhang, P., 2021. Koszul modules (and the Omega-growth of modules) over short local algebras. Journal of Pure and Applied Algebra, 225(12): 106772.
C.M. Ringel and P. Zhang, “Koszul modules (and the Omega-growth of modules) over short local algebras”, Journal of Pure and Applied Algebra, vol. 225, 2021, : 106772.
Ringel, C.M., Zhang, P.: Koszul modules (and the Omega-growth of modules) over short local algebras. Journal of Pure and Applied Algebra. 225, : 106772 (2021).
Ringel, Claus Michael, and Zhang, Pu. “Koszul modules (and the Omega-growth of modules) over short local algebras”. Journal of Pure and Applied Algebra 225.12 (2021): 106772.

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