Nakayama algebra

In algebra, a Nakayama algebra or generalized uniserial algebra is an algebra such that the left and right projective modules have 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, Tadasi (1940), "Note on uni-serial and generalized uni-serial rings", Proc. Imp. Acad. Tokyo 16: 285–289, MR 0003618 
• Reiten, Idun (1982), "The use of almost split sequences in the representation theory of Artin algebras", Representations of algebras (Puebla, 1980), Lecture Notes in Math. 944, Berlin, New York: Springer-Verlag, pp. 29–104, doi:10.1007/BFb0094057, MR 672115