The Short Local Algebras of Dimension 6 with Non-projective Reflexive Modules
Ringel CM (2023)
Communications in Mathematics and Statistics volume 11(2): 195-227.
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Abstract / Bemerkung
Let A be a finite-dimensional local algebra over an algebraically closed field, let J be the radical of A. The modules we are interested in are the finitely generated left A-modules. Projective modules are always reflexive, and an algebra is self-injective iff all modules are reflexive. We discuss the existence of non-projective reflexive modules in case A is not self-injective. We assume that A is short (this means that J(3 )= 0). In a joint paper with Zhang Pu, it has been shown that 6 is the smallest possible dimension of A that can occur and that in this case the following conditions have to be satisfied: J(2) is both the left socle and the right socle of A and there is no uniform ideal of length 3. The present paper is devoted to showing the converse.
Stichworte
Short local algebra;
Reflexive module;
Gorenstein-projective module;
Bristle;
Atom;
Bar;
Bristle-bar layout
Erscheinungsjahr
2023
Zeitschriftentitel
Communications in Mathematics and Statistics volume
Band
11
Ausgabe
2
Seite(n)
195-227
Urheberrecht / Lizenzen
ISSN
2194-6701
eISSN
2194-671X
Finanzierungs-Informationen
Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.
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https://pub.uni-bielefeld.de/record/2979988
Zitieren
Ringel CM. The Short Local Algebras of Dimension 6 with Non-projective Reflexive Modules. Communications in Mathematics and Statistics volume. 2023;11(2):195-227.
Ringel, C. M. (2023). The Short Local Algebras of Dimension 6 with Non-projective Reflexive Modules. Communications in Mathematics and Statistics volume, 11(2), 195-227. https://doi.org/10.1007/s40304-023-00343-9
Ringel, Claus Michael. 2023. “The Short Local Algebras of Dimension 6 with Non-projective Reflexive Modules”. Communications in Mathematics and Statistics volume 11 (2): 195-227.
Ringel, C. M. (2023). The Short Local Algebras of Dimension 6 with Non-projective Reflexive Modules. Communications in Mathematics and Statistics volume 11, 195-227.
Ringel, C.M., 2023. The Short Local Algebras of Dimension 6 with Non-projective Reflexive Modules. Communications in Mathematics and Statistics volume, 11(2), p 195-227.
C.M. Ringel, “The Short Local Algebras of Dimension 6 with Non-projective Reflexive Modules”, Communications in Mathematics and Statistics volume, vol. 11, 2023, pp. 195-227.
Ringel, C.M.: The Short Local Algebras of Dimension 6 with Non-projective Reflexive Modules. Communications in Mathematics and Statistics volume. 11, 195-227 (2023).
Ringel, Claus Michael. “The Short Local Algebras of Dimension 6 with Non-projective Reflexive Modules”. Communications in Mathematics and Statistics volume 11.2 (2023): 195-227.
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