A family of noetherian rings with their finite length modules under control

Title:

A family of noetherian rings with their finite length modules under control

Creator:

Schmidmeier, Markus

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:ec0d7ea8-e4ff-46b8-8781-5b4b985b0003
uuid:ec0d7ea8-e4ff-46b8-8781-5b4b985b0003

Subject:

V-ring, progenerator, and almost split morphisms

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We investigate the category $\text{mod}\Lambda $ of finite length modules over the ring $\Lambda =A\otimes _k\Sigma $, where $\Sigma $ 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 $P_j=A\otimes E_j$. By a result of K. Fuller, $P_j$ induces a category equivalence from which we deduce that $\text{mod}\Lambda \simeq \coprod _jbad hbox P_j$. As a consequence we can (1) construct for each elementary $k$-algebra $A$ over a finite field $k$ a nonartinian noetherian ring $\Lambda $ such that $\text{mod}A\simeq \text{mod}\Lambda $, (2) find twisted versions $\Lambda $ of algebras of wild representation type such that $\Lambda $ itself is of finite or tame representation type (in mod), (3) describe for certain rings $\Lambda $ the minimal almost split morphisms in $\text{mod} \Lambda $ and observe that almost all of these maps are not almost split in $\text{Mod}\Lambda $.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

545-552

Source:

Czechoslovak Mathematical Journal | 2002 Volume:52 | Number:3

Harvested from:

CDK

Metadata only:

false