Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Nakayama algebras and graded trees

Authors: B. Rohnes and S. O. Smalø
Journal: Trans. Amer. Math. Soc. 279 (1983), 249-256
MSC: Primary 16A64; Secondary 16A46
MathSciNet review: 704614
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ k$ be an algebraically closed field. We show that if $ T$ is a finite tree, then there is a grading $ g$ on $ T$ such that $ (T,g)$ is a representation finite graded tree, and such that the corresponding simply connected $ k$-algebra is a Nakayama algebra (i.e. generalized uniserial algebra).

References [Enhancements On Off] (What's this?)

  • [1] M. Auslander and I. Reiten, Representation theory of artin algebras. IV; Invariants given by almost split sequences, Comm. Algebra 5 (1977), 443-518. MR 0439881 (55:12762)
  • [2] K. Bongartz and P. Gabriel, Covering spaces in the representation theory, Invent. Math. 65 (1982), 331-378. MR 643558 (84i:16030)
  • [3] P. Gabriel, The universal cover of a representation-finite algebra, Proc. Third Internat. Conf. Rep. Algebra, Puebla, 1980. MR 654725 (83f:16036)
  • [4] H. Kupisch, Beiträge zur Theorie nichthalbeinfacher Ringe mit Minimalbedingung, J. Reine Angew. Math. 201 (1959), 100-112. MR 0104707 (21:3460)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 16A64, 16A46

Retrieve articles in all journals with MSC: 16A64, 16A46

Additional Information

Keywords: Simply connected algebra, module, graded tree, Kupisch series
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society