algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...

, a Nakayama algebra or generalized uniserial algebra is an

such that each left or right indecomposable projective module has a unique

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 natura ...

. They were studied by who called them "generalized uni-serial rings". These algebras were further studied by and later by , by and by . An example of a Nakayama algebra is ''k'' 'x''(''x''^''n'') for ''k'' a

field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grass ...

and ''n'' a positive

integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ...

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

here Here is an adverb that means "in, on, or at this place". It may also refer to: Software * Here Technologies, a mapping company * Here WeGo (formerly Here Maps), a mobile app and map website by Here Technologies, Here Television * Here TV (form ...

References

* * * * *{{Citation , last1=Reiten , first1=Idun , title=Representations of algebras (Puebla, 1980) , publisher=

Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 ...

, location=Berlin, New York , series=Lecture Notes in Mathematics , doi=10.1007/BFb0094057 , mr=672115 , year=1982 , volume=944 , chapter=The use of almost split sequences in the representation theory of Artin algebras , pages=29–104, isbn=978-3-540-11577-9 Ring theory