Submodule categories of wild representation type |
| |
Authors: | Claus Michael Ringel |
| |
Affiliation: | a Fakultät für Mathematik, Universität Bielefeld, P.O. Box 100131, D-33501 Bielefeld, Germany b Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, Florida 33431-0991, USA |
| |
Abstract: | Let Λ be a commutative local uniserial ring with radical factor field k. We consider the category S(Λ) of embeddings of all possible submodules of finitely generated Λ-modules. In case Λ=Z/〈pn〉, where p is a prime, the problem of classifying the objects in S(Λ), up to isomorphism, has been posed by Garrett Birkhoff in 1934. In this paper we assume that Λ has Loewy length at least seven. We show that S(Λ) is controlled k-wild with a single control object I∈S(Λ). It follows that each finite dimensional k-algebra can be realized as a quotient End(X)/End(X)I of the endomorphism ring of some object X∈S(Λ) modulo the ideal End(X)I of all maps which factor through a finite direct sum of copies of I. |
| |
Keywords: | Primary: 16G60 secondary: 20K27, 47A15 |
本文献已被 ScienceDirect 等数据库收录! |
|