In algebra, a Nakayama algebra or generalized uniserial algebra is an algebra such that each left or right indecomposable projective module has a unique composition series (Reiten 1982, p. 39). They were studied by Tadasi Nakayama (1940) 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.
References
Nakayama algebra Wikipedia(Text) CC BY-SA