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UBC Theses and Dissertations

Finitely presented modules and stable theory Gentle, Ronald Stanley

Abstract

This thesis is a two pronged affair. Part one is a study of finitely presented modules using the techniques of homological algebra. We establish a theorem involving certain exact sequences, which proves to be highly efficient in dealing with the theory of finitely presented modules. An attempt has been made to unify many of the results found in the literature, (with the inclusion of some original results). Part two, which can he read independently of part one, is a study of the category of short exact sequences modulo split sequences. Special attention is paid to projectives in this category; an explicit construction of a projective resolution, with its' consequences, for an arbitrary object is given. Part two is related to part one in providing a categorical bedding, thereby enriching the theory of finitely presented modules.

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