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Model Theory and Modules
, 2006
"... The modeltheoretic investigation of modules has led to ideas, techniques and results which are of algebraic interest, irrespective of their modeltheoretic significance. It is these aspects that I will discuss in this article, although I will make some comments on the model theory of modules per se ..."
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Cited by 64 (20 self)
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The modeltheoretic investigation of modules has led to ideas, techniques and results which are of algebraic interest, irrespective of their modeltheoretic significance. It is these aspects that I will discuss in this article, although I will make some comments on the model theory of modules per se. Our default is that the term “module ” will mean (unital) right module over a ring (associative with 1) R. The category of such modules is denoted ModR, the full subcategory of finitely presented modules will be denoted modR, the
The Ziegler and Zariski spectra of some domestic string algebras
 Theory
, 1999
"... It was a conjecture of the second author that the CantorBendixson rank of the Ziegler spectrum of a nitedimensional algebra is either less than or equal to 2 or is undened. Here we refute this conjecture by describing the Ziegler spectra of some domestic string algebras where arbitrary nite va ..."
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Cited by 12 (9 self)
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It was a conjecture of the second author that the CantorBendixson rank of the Ziegler spectrum of a nitedimensional algebra is either less than or equal to 2 or is undened. Here we refute this conjecture by describing the Ziegler spectra of some domestic string algebras where arbitrary nite values greater than 2 are obtained. We give a complete description of the Ziegler and GabrielZariski spectra of the simplest of these algebras. The conjecture has been independently refuted by Schroer [21] who, extending his work [20] on these algebras, computed their KrullGabriel dimension. 1 Indecomposable pureinjectives over domestic string algebras 12 Let R be a domestic string algebra over an arbitrary eld k. Modules will generally be left Rmodules: the category of these we denote by RMod. 1 This work was done while the rst author was supported by EPSRC grant number GR/K19686. Both authors thank the EPSRC for this nancial support. 2 Primary: 16G20; Secondary: 03C60,...
Modules With Few Types Over Some FiniteDimensional Algebras
"... Using the description of the Ziegler spectrum we characterise modules with various stabilitytheoretic properties (!stability, superstability, categoricity) over certain classes of finitedimensional algebras. We also ..."
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Using the description of the Ziegler spectrum we characterise modules with various stabilitytheoretic properties (!stability, superstability, categoricity) over certain classes of finitedimensional algebras. We also