Gorenstein-projective and semi-Gorenstein-projective modules

Ringel CM, Zhang P (2020)
ALGEBRA & NUMBER THEORY 14(1): 1-36.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Autor*in
Abstract / Bemerkung
Let A be an artin algebra. An A-module M will be said to be semi-Gorenstein-projective provided that Ext(i) (M, A) = 0 for all i >= 1. All Gorenstein-projective modules are semi-Gorenstein-projective and only few and quite complicated examples of semi-Gorenstein-projective modules which are not Gorenstein-projective have been known. One of the aims of the paper is to provide conditions on A such that all semi-Gorenstein-projective left modules are Gorenstein-projective (we call such an algebra left weakly Gorenstein). In particular, we show that in case there are only finitely many isomorphism classes of indecomposable left modules which are both semi-Gorenstein-projective and torsionless, then A is left weakly Gorenstein. On the other hand, we exhibit a 6-dimensional algebra 3 with a semi-Gorenstein-projective module M which is not torsionless (thus not Gorenstein-projective). Actually, also the 3-dual module M* is semi-Gorenstein-projective. In this way, we show the independence of the total reflexivity conditions of Avramov and Martsinkovsky, thus completing a partial proof by Jorgensen and Sega. Since all the syzygy-modules of M and M* are 3-dimensional, the example can be checked (and visualized) quite easily.
Stichworte
Gorenstein-projective module; semi-Gorenstein-projective module; left; weakly Gorenstein algebra; torsionless module; reflexive module; t-torsionfree module; Frobenius category; (sic)-quiver
Erscheinungsjahr
2020
Zeitschriftentitel
ALGEBRA & NUMBER THEORY
Band
14
Ausgabe
1
Seite(n)
1-36
ISSN
1937-0652
eISSN
1944-7833
Page URI
https://pub.uni-bielefeld.de/record/2942744

Zitieren

Ringel CM, Zhang P. Gorenstein-projective and semi-Gorenstein-projective modules. ALGEBRA & NUMBER THEORY. 2020;14(1):1-36.
Ringel, C. M., & Zhang, P. (2020). Gorenstein-projective and semi-Gorenstein-projective modules. ALGEBRA & NUMBER THEORY, 14(1), 1-36. doi:10.2140/ant.2020.14.1
Ringel, C. M., and Zhang, P. (2020). Gorenstein-projective and semi-Gorenstein-projective modules. ALGEBRA & NUMBER THEORY 14, 1-36.
Ringel, C.M., & Zhang, P., 2020. Gorenstein-projective and semi-Gorenstein-projective modules. ALGEBRA & NUMBER THEORY, 14(1), p 1-36.
C.M. Ringel and P. Zhang, “Gorenstein-projective and semi-Gorenstein-projective modules”, ALGEBRA & NUMBER THEORY, vol. 14, 2020, pp. 1-36.
Ringel, C.M., Zhang, P.: Gorenstein-projective and semi-Gorenstein-projective modules. ALGEBRA & NUMBER THEORY. 14, 1-36 (2020).
Ringel, Claus Michael, and Zhang, Pu. “Gorenstein-projective and semi-Gorenstein-projective modules”. ALGEBRA & NUMBER THEORY 14.1 (2020): 1-36.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Suchen in

Google Scholar