On minimal representation-infinite algebras
Klaus Bongartz
TL;DR
This paper classifies all minimal representation-infinite algebras with non-distributive ideal lattices over algebraically closed fields, showing finitely many such classes exist in each dimension.
Contribution
It provides a complete classification of minimal representation-infinite algebras with non-distributive ideal lattices, a previously unresolved problem.
Findings
Finitely many isomorphism classes in each dimension
Complete classification of minimal representation-infinite algebras with non-distributive lattices
Identification of structural properties of these algebras
Abstract
Over an algebraically closed field we classify all minimal representation-infinite algebras where the lattice of two-sided ideals is not distributive. As a consequence there are only finitely many isomorphism classes of minimal representation-infinite algebras in each dimension.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Algebra and Logic · Advanced Topology and Set Theory