Results 1  10
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13
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
Topological and Geometric aspects of the Ziegler Spectrum
, 1998
"... The aim here is to emphasise the topological and geometric structure that the Ziegler spectrum carries and to illustrate how this structure may be used in the analysis of particular examples. There is not space here for me to give a survey of what is known about the Ziegler spectrum so there are ..."
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Cited by 6 (5 self)
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The aim here is to emphasise the topological and geometric structure that the Ziegler spectrum carries and to illustrate how this structure may be used in the analysis of particular examples. There is not space here for me to give a survey of what is known about the Ziegler spectrum so there are a number of topics that I will just mention in order to give some indication of what lies beyond what is discussed here. 1. The Ziegler spectrum 2. Various dimensions 3. These dimensions for artin algebras 4. These dimensions in general 5. Duality 6. The complexity of morphisms in modR 7. The GabrielZariski topology 8. The sheaf of locally definable scalars 1 The Ziegler spectrum 1.1 A reminder on purity and pureinjectives Suppose that M is a submodule of N . Consider a finite system \Sigma n i=1 x i r ij = a j (j = 1; :::m) of Rlinear equations over M : that is, the r ij are in R, the 1 a j are in M and the x i are indeterminates. Suppose that there is a solution b 1 ; ...
Modeltheoretic imaginaries and coherent sheaves
, 2006
"... In this paper we attempt to bridge a gap or, perhaps, to strengthen some existing links. Model theory has evolved in two sharply different directions. One is setbased, centred ..."
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Cited by 3 (2 self)
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In this paper we attempt to bridge a gap or, perhaps, to strengthen some existing links. Model theory has evolved in two sharply different directions. One is setbased, centred
MODELTHEORETIC IMAGINARIES AND ZIEGLER SPECTRA IN GENERAL CATEGORIES
"... 2.1 Overview.................................. 14 2.2 Finitely generated, finitely presented and coherent objects...... 14 ..."
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2.1 Overview.................................. 14 2.2 Finitely generated, finitely presented and coherent objects...... 14
Positive Imaginaries and Coherent Affine Functors
, 2007
"... The starting point for the ideas in this paper is a result of Kevin Burke [2, Prop 3.2.5] in the model theory of modules. This result establishes a correspondence between syntactically defined “ppimaginaries ” and certain, ..."
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The starting point for the ideas in this paper is a result of Kevin Burke [2, Prop 3.2.5] in the model theory of modules. This result establishes a correspondence between syntactically defined “ppimaginaries ” and certain,
DEFINABLE ADDITIVE CATEGORIES
, 2008
"... This is essentially the talk I gave on definable additive categories; I define these categories, say where they came from, describe some of what is around them and then point out the 2category which they form. ..."
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This is essentially the talk I gave on definable additive categories; I define these categories, say where they came from, describe some of what is around them and then point out the 2category which they form.