Artin algebras are a class of associative algebras that have several important properties in representation theory and algebra. Specifically, an Artin algebra is defined as a finite-dimensional algebra over a field that satisfies certain conditions. Here are some key features of Artin algebras: 1. **Finite Length**: An Artin algebra has the property that as a module over itself, it has finite length. This means that it has a composition series with a finite number of simple submodules.
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