The relevance and the ubiquity of Prüfer modules

Ringel CM (2009)
In: Representation theory. Fourth international conference on representation theory, Lhasa, China, July 16-20, 2007. Lin Z, Wang J (Eds); Contemporary Mathematics, 478. Providence, RI: American Mathematical Society (AMS): 163-175.

Konferenzbeitrag | Veröffentlicht | Englisch
 
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Herausgeber*in
Lin, Zongzhu; Wang, Jianpan
Abstract / Bemerkung
Let R be a ring. An R-module M is called a Prüfer module provided there exists a locally nilpotent, surjective endomorphism of M with kernel of finite length. We want to outline the relevance, but also the ubiquity of Prüfer modules. The main assertion will be that any Prüfer module which is not of finite type gives rise to a generic module,thus to infinite families of indecomposable modules with fixed endo-length (here we are in the setting of the second Brauer-Thrall conjecture). In addition, we will report on a construction procedure which yields a wealth of Prüfer modules. Unfortunately, we do not know which modules obtained in this way are of finite type.
Erscheinungsjahr
2009
Titel des Konferenzbandes
Representation theory. Fourth international conference on representation theory, Lhasa, China, July 16-20, 2007
Band
478
Seite(n)
163-175
Konferenz
Fourth international conference on representation theory
Konferenzort
Lhasa, China
Konferenzdatum
2007-07-16 – 2007-07-20
ISBN
978-0-8218-4555-4
Page URI
https://pub.uni-bielefeld.de/record/2940868

Zitieren

Ringel CM. The relevance and the ubiquity of Prüfer modules. In: Lin Z, Wang J, eds. Representation theory. Fourth international conference on representation theory, Lhasa, China, July 16-20, 2007. Contemporary Mathematics. Vol 478. Providence, RI: American Mathematical Society (AMS); 2009: 163-175.
Ringel, C. M. (2009). The relevance and the ubiquity of Prüfer modules. In Z. Lin & J. Wang (Eds.), Contemporary Mathematics: Vol. 478. Representation theory. Fourth international conference on representation theory, Lhasa, China, July 16-20, 2007 (pp. 163-175). Providence, RI: American Mathematical Society (AMS).
Ringel, C. M. (2009). “The relevance and the ubiquity of Prüfer modules” in Representation theory. Fourth international conference on representation theory, Lhasa, China, July 16-20, 2007, Lin, Z., and Wang, J. eds. Contemporary Mathematics, vol. 478, (Providence, RI: American Mathematical Society (AMS), 163-175.
Ringel, C.M., 2009. The relevance and the ubiquity of Prüfer modules. In Z. Lin & J. Wang, eds. Representation theory. Fourth international conference on representation theory, Lhasa, China, July 16-20, 2007. Contemporary Mathematics. no.478 Providence, RI: American Mathematical Society (AMS), pp. 163-175.
C.M. Ringel, “The relevance and the ubiquity of Prüfer modules”, Representation theory. Fourth international conference on representation theory, Lhasa, China, July 16-20, 2007, Z. Lin and J. Wang, eds., Contemporary Mathematics, vol. 478, Providence, RI: American Mathematical Society (AMS), 2009, pp.163-175.
Ringel, C.M.: The relevance and the ubiquity of Prüfer modules. In: Lin, Z. and Wang, J. (eds.) Representation theory. Fourth international conference on representation theory, Lhasa, China, July 16-20, 2007. Contemporary Mathematics. 478, p. 163-175. American Mathematical Society (AMS), Providence, RI (2009).
Ringel, Claus Michael. “The relevance and the ubiquity of Prüfer modules”. Representation theory. Fourth international conference on representation theory, Lhasa, China, July 16-20, 2007. Ed. Zongzhu Lin and Jianpan Wang. Providence, RI: American Mathematical Society (AMS), 2009.Vol. 478. Contemporary Mathematics. 163-175.

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