A note on preprojective partitions over hereditary Artin algebras

Author:
Gordana Todorov

Journal:
Proc. Amer. Math. Soc. **85** (1982), 523-528

MSC:
Primary 16A35

DOI:
https://doi.org/10.1090/S0002-9939-1982-0660596-0

MathSciNet review:
660596

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Abstract: If is an artin algebra there is a partition of , the category of indecomposable finitely generated -modules, , called the preprojective partition. We show that can be easily constructed for hereditary artin algebras, if is known: is in if and only if is not in and there is an irreducible map , where is in .

**[1]**M. Auslander and I. Reiten,*Representation theory of artin algebras*. IV.*Invariants given by almost split sequences*, Comm. Algebra**5**(1977), 441-518. MR**0439881 (55:12762)****[2]**M. Auslander and S. Smalø,*Preprojective modules over artin algebras*, J. Algebra**66**(1980), 61-122. MR**591246 (83a:16039)****[3]**-,*Preprojective modules: an introduction and some applications*, Lecture Notes in Math., Vol. 831, Springer-Verlag, Berlin and New York, 1979, pp. 48-73. MR**607148 (82i:16027)****[4]**D. Zacharia,*The preprojective partitions for hereditary artin algebras*, Ph.D. Thesis, Brandeis University, 1981. MR**670936 (84a:16030)**

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DOI:
https://doi.org/10.1090/S0002-9939-1982-0660596-0

Article copyright:
© Copyright 1982
American Mathematical Society