Transfinite tree quivers and their representations

Details Transfinite tree quivers and their representations Transfinite tree quivers and their representations

2012-01-11

arxiv.org/abs/1201.2294v1

Mathematics

Rings and Algebras

to appear in Mathematica Scandinavica

Scientific paper

The idea of "vertex at the infinity" naturally appears when studying indecomposable injective representations of tree quivers. In this paper we formalize this behavior and find the structure of all the indecomposable injective representations of a tree quiver of size an arbitrary cardinal $\kappa$. As a consequence the structure of injective representations of noetherian $\kappa$-trees is completely determined. In the second part we will consider the problem whether arbitrary trees are source injective representation quivers or not.

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