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

MathSciNet review:
0376768

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Abstract | References | Similar Articles | Additional Information

Abstract: Tachikawa has shown that if a ring 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.

**[1]**F. W. Anderson and K. R. Fuller,*Modules with decompositions that complement direct summands*, J. Algebra**22**(1972), 241–253. MR**0301051****[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]**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****[5]**Manabu Harada and Youshin Sai,*On categories of indecomposable modules. I*, Osaka J. Math.**7**(1970), 323–344. MR**0286859****[6]**Hiroyuki Tachikawa,*𝑄𝐹-3 rings and categories of projective modules*, J. Algebra**28**(1974), 408–413. MR**0432696**

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DOI:
http://dx.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