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Note on rings of finite representation type and decompositions of modules


Authors: K. R. Fuller and Idun Reiten
Journal: Proc. Amer. Math. Soc. 50 (1975), 92-94
MSC: Primary 16A64
DOI: https://doi.org/10.1090/S0002-9939-1975-0376768-5
MathSciNet review: 0376768
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Abstract: Tachikawa has shown that if a ring $ \Lambda $ is of finite representation type, then each of its left and right modules has a decomposition that complements direct summands. We show that the converse is also true.


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

  • [1] F. W. Anderson and K. R. Fuller, Modules with decompositions that complement direct summands, J. Algebra 22 (1972), 241-253. MR 46 #209. MR 0301051 (46:209)
  • [2] M. Auslander, Representation dimension of Artin algebras, Queen Mary College Notes, London, 1971.
  • [3] -, Representation theory of Artin algebras. II, Communications in Algebra 1 (1974), 293-310.
  • [4] M. Auslander and M. Bridger, Stable module theory, Mem. Amer. Math. Soc. No. 94 (1969). MR 42 #4580. MR 0269685 (42:4580)
  • [5] M. Harada and Y. Sai, On categories of indecomposable modules. I, Osaka J. Math. 7 ( 1970), 323-344. MR 44 #4066. MR 0286859 (44:4066)
  • [6] H. Tachikawa, QF-$ 3$ rings and categories of projective modules, J. Algebra 28 (1974), 408-413. MR 0432696 (55:5682)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0376768-5
Keywords: Finite representation type, transpose, dual, decompositions of modules
Article copyright: © Copyright 1975 American Mathematical Society

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