- References
In mathematics, Nakayama's conjecture is a conjecture about Artinian rings, introduced by {{harvs|txt|last=Nakayama|authorlink=Tadasi Nakayama|year=1958}}. The generalized Nakayama conjecture is an extension to more general rings, introduced by {{harvs|txt|last=Auslander|last2=Reiten|year=1975}}. {{harvtxt|Leuschke|Huneke|2004}} proved some cases of the generalized Nakayama conjecture. Nakayama's conjecture states that if all the modules of a minimal injective resolution of an Artin algebra R are injective and projective, then R is self-injective. References- {{Citation | last1=Auslander | first1=Maurice | last2=Reiten | first2=Idun | title=On a generalized version of the Nakayama conjecture | jstor=2040102 |mr=0389977 | year=1975 | journal=Proceedings of the American Mathematical Society | issn=0002-9939 | volume=52 | issue=1 | pages=69–74 | doi=10.2307/2040102}}
- {{Citation | last1=Leuschke | first1=Graham J. | last2=Huneke | first2=Craig | title=On a conjecture of Auslander and Reiten | doi=10.1016/j.jalgebra.2003.07.018 |mr=2052636 | year=2004 | journal=Journal of Algebra | issn=0021-8693 | volume=275 | issue=2 | pages=781–790}}
- {{Citation | last1=Nakayama | first1=Tadasi | title=On algebras with complete homology | doi=10.1007/BF02941960 |mr=0104718 | year=1958 | journal=Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg | issn=0025-5858 | volume=22 | pages=300–307}}
{{abstract-algebra-stub}} 1 : Ring theory |