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Transactions of the American Mathematical Society

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Stable equivalence for some categories with radical square zero


Author: Idun Reiten
Journal: Trans. Amer. Math. Soc. 212 (1975), 333-345
MSC: Primary 18E05
DOI: https://doi.org/10.1090/S0002-9947-1975-0382396-2
MathSciNet review: 0382396
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Abstract: For certain abelian categories with radical square zero, containing artin rings with radical square zero as a special case, we give a way of constructing hereditary abelian categories stably equivalent to them, i.e. such that their categories modulo projectives are equivalent categories.


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

  • [1] M. Auslander, Representation dimension of artin algebras, Queen Mary College Notes, 1971.
  • [2] -, Representation theory of artin algebras. I, Comm. Algebra 1 (1974), 177-268. MR 0349747 (50:2240)
  • [3] M. Auslander and I. Reiten, Stable equivalence of artin algebras, Proc. Conf. on Orders, Group Rings and Related Topics, 1973, pp. 8-70. MR 0335575 (49:356)
  • [4] M. Auslander and I. Reiten, Stable equivalence of dualizing R-varieties, Advances in Math. 12 (1974), 306-366. MR 0342505 (49:7251)
  • [5] -, Stable equivalence of dualizing R-varieties. III: Dualizing R-varieties stably equivalent to hereditary R-varieties, Advances in Math. 17 (1975).
  • [6] R. Fossum, P. Griffith and I. Reiten, Homological algebra of trivial extensions of abelian categories with applications to ring theory, Lecture Notes in Math., vol. 456, Springer-Verlag, Berlin and New York, 1975. MR 0389981 (52:10810)

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DOI: https://doi.org/10.1090/S0002-9947-1975-0382396-2
Article copyright: © Copyright 1975 American Mathematical Society

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