Nakayama algebra

Summary

A Nakayama algebra is a finite-dimensional algebra whose indecomposable projective modules, on both sides, are uniserial: their submodules form a single chain. Nakayama studied them under the name generalized uniserial algebras, and they are now named after him. Every indecomposable module over a Nakayama algebra is uniserial, so the algebra has only finitely many indecomposable modules up to isomorphism. They are one of the few classes of algebras whose modules can be listed completely, and they serve as a test case in representation theory.