Fix R = k[[x]]. Let Q<sub>n</sub> be the category whose objects are ((M₁,...,M<sub>n</sub>),(f₁,...,f<sub>n-1</sub>)) where each M<sub>i</sub> is a free R-module and f<sub>i</sub>:M<sub>i</sub>⟶M<sub>i+1</sub> for each i=1,...,n-1, and in which the morphisms are the obvious ones. Let β<sub>n</sub> be the full subcategory of Ω<sub>n</sub> in which each map f<sub>i</sub> is a monomorphism whose cokernel is a torsion module. It is shown that there is a full dense functor Ω<sub>n</sub>⟶β<sub>n</sub>. If X is an object of β<sub>n</sub>, we say that X <u>diagonalizes</u> if X is isomorphic to a direct sum of objects ((M₁,...,M<sub>n</sub>),(f₁,...,f<sub>n-1</sub>)) in which each M<sub>i</sub> is of rank one. We establish an algorithm which diagonalizes any diagonalizable object X of β<sub>n</sub>, and which fails only in case X is not diagonalizable.
Let Λ be an artin algebra of finite type. We prove that for a fixed C in mod(Λ) there are only finitely many modules A in mod(Λ) (up to isomorphism) for which a short exact sequence of the form 0⟶A⟶B⟶C⟶0 is indecomposable. / Ph. D. / incomplete_metadata
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/50001 |
| Date | January 1986 |
| Creators | Corwin, Stephen P. |
| Contributors | Mathematics, Green, Edward, Farkas, Daniel R., Wheeler, Robert, Aull, Charles E., Brown, E.A. |
| Publisher | Virginia Polytechnic Institute and State University |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | v, 65 leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 14701354 |
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