A family of noetherian rings with their finite length modules under control |
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Authors: | Markus Schmidmeier |
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Institution: | (1) Dept. of Math. Sciences, Florida Atlantic University, Boca Raton, Florida, 33431-0991, U.S.A |
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Abstract: | We investigate the category mod of finite length modules over the ring =A
k
, where 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 mod 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 such that modA mod(2) find twisted versions of algebras of wild representation type such that itself is of finite or tame representation type (in mod)(3) describe for certain rings the minimal almost split morphisms in mod and observe that almost all of these maps are not almost split in Mod. |
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Keywords: | V-ring progenerator almost split morphisms |
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