In algebra, a Nakayama algebra or generalized uniserial algebra is an algebra such that the left and right projective module

Projective module

In mathematics, particularly in abstract algebra and homological algebra, the concept of projective module over a ring R is a more flexible generalisation of the idea of a free module...

s have a unique composition series

Composition series

In abstract algebra, a composition series provides a way to break up an algebraic structure, such as a group or a module, into simple pieces. The need for considering composition series in the context of modules arises from the fact that many naturally occurring modules are not semisimple, hence...

 . They were studied by who called them "generalized uni-serial rings".

An example of a Nakayama algebra is k[x]/(xⁿ) for k a field and n a positive integer.

Current usage of uniserial differs slightly: an explanation of the difference appears here.