Kronecker modules generated by modules of length 2
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Let $\Lambda$ be a ring and $\mathcal N$ a class of $\Lambda$-modules. A $\Lambda$-module is said to be generated by $\mathcal N$ provided that it is a factor module of a direct sum of modules in $\mathcal N$. The semi-simple $\Lambda$-modules are just the $\Lambda$-modules which are generated by the $\Lambda$-modules of length 1. It seems that the modules which are generated by the modules of length $2$ (we call them bristled modules) have not attracted the interest they deserve.
In this paper we deal with the basic case of the Kronecker modules, these are the (finite-dimensional) representations of an $n$-Kronecker quiver, where $n$ is a natural number. We show that for $n\ge 3$, there is an abundance of bristled Kronecker modules.
[1] P. Fahr,et al. A Partition Formula for Fibonacci Numbers , 2008 .
[2] C. Ringel. The eigenvector variety of a matrix pencil , 2017, 1703.04097.
[3] C. Ringel. Tame Algebras and Integral Quadratic Forms , 1985 .
[4] C. Ringel,et al. Categorification of the Fibonacci numbers using representations of quivers , 2011, 1107.1858.