These notes present an introduction into the spectrum of the category of modules over a ring. We discuss the general theory of pure-injective modules and concentrate on the isomorphism classes of indecomposable pure-injective modules which form the underlying set of this spectrum. The interplay between the spectrum and the category of finitely presented modules provides new insight into the geometrical and homological properties of the category of finitely presented modules. Various applications from representation theory of finite dimensional algebras are included.
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Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
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ISBN-13
978-0-8218-2618-8 (9780821826188)
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Schweitzer Klassifikation
Introduction The functor category Definable subcategories Left approximations duality Ideals in the category of finitely presented modules Endofinite modules Krull-Gabriel dimension The infinite radical Functors between module categories Tame algebras Rings of definable scalars Reflective definable subcategories Sheaves Tame hereditary algebras Coherent rings Appendix A. Locally coherent Grothendieck categories Appendix B. Dimensions Appendix C. Finitely presented functors and ideals Bibliography.
