Note on rings of finite representation type and decompositions of modules
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- by K. R. Fuller and Idun Reiten PDF
- Proc. Amer. Math. Soc. 50 (1975), 92-94 Request permission
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
- F. W. Anderson and K. R. Fuller, Modules with decompositions that complement direct summands, J. Algebra 22 (1972), 241–253. MR 301051, DOI 10.1016/0021-8693(72)90145-7 M. Auslander, Representation dimension of Artin algebras, Queen Mary College Notes, London, 1971. —, Representation theory of Artin algebras. II, Communications in Algebra 1 (1974), 293-310.
- Maurice Auslander and Mark Bridger, Stable module theory, Memoirs of the American Mathematical Society, No. 94, American Mathematical Society, Providence, R.I., 1969. MR 0269685
- Manabu Harada and Youshin Sai, On categories of indecomposable modules. I, Osaka Math. J. 7 (1970), 323–344. MR 286859
- Hiroyuki Tachikawa, $QF-3$ rings and categories of projective modules, J. Algebra 28 (1974), 408–413. MR 432696, DOI 10.1016/0021-8693(74)90049-0
Additional Information
- © Copyright 1975 American Mathematical Society
- 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