Huisgen-Zimmermann, Birge The geometry of uniserial representations of finite dimensional algebras. III: Finite uniserial type. (English) Zbl 0862.16008 Trans. Am. Math. Soc. 348, No. 12, 4775-4812 (1996). Summary: [Part I of this paper is submitted, part II is in preparation.]A description is given of those sequences \({\mathbf S}=(S(0),S(1),\dots,S(l))\) of simple modules over a finite dimensional algebra for which there are only finitely many uniserial modules with consecutive composition factors \(S(0),\dots,S(l)\). Necessary and sufficient conditions for an algebra to permit only a finite number of isomorphism types of uniserial modules are derived. The main tools in this investigation are the affine algebraic varieties parametrizing the uniserial modules with composition series \({\mathbf S}\). Cited in 3 ReviewsCited in 11 Documents MSC: 16G30 Representations of orders, lattices, algebras over commutative rings 16G60 Representation type (finite, tame, wild, etc.) of associative algebras 16P10 Finite rings and finite-dimensional associative algebras Keywords:simple modules; finite dimensional algebras; uniserial modules; composition factors; affine algebraic varieties; composition series PDFBibTeX XMLCite \textit{B. Huisgen-Zimmermann}, Trans. Am. Math. Soc. 348, No. 12, 4775--4812 (1996; Zbl 0862.16008) Full Text: DOI arXiv