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- W1592010664 abstract "We investigate the category modΛ of finite length modules over the ring Λ=A ⊗ k Σ, where Σ is a V-ring, i.e. a ring for which every simple module is injective, k a subfield of its centre and A an elementary k-algebra. Each simple module E j gives rise to a quasiprogenerator P j = A ⊗ E j . By a result of K. Fuller, P j induces a category equivalence from which we deduce that modΛ ≃ ∐j mod EndP j . As a consequence we can (1) construct for each elementary k-algebra A over a finite field k a nonartinian noetherian ring Λ such that modA ≃ modΛ (2) find twisted versions Λ of algebras of wild representation type such that Λ itself is of finite or tame representation type (in mod) (3) describe for certain rings Λ the minimal almost split morphisms in modΛ and observe that almost all of these maps are not almost split in ModΛ." @default.
- W1592010664 created "2016-06-24" @default.
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- W1592010664 date "2002-09-01" @default.
- W1592010664 modified "2023-10-11" @default.
- W1592010664 title "A family of noetherian rings with their finite length modules under control" @default.
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- W1592010664 doi "https://doi.org/10.1023/a:1021723728841" @default.
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