Prerequisites in Module Theory

Peter Schneider
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Peter Schneider: University of Münster, Department of Mathematics

Chapter Chapter 1 in Modular Representation Theory of Finite Groups, 2013, pp 1-41 from Springer

Abstract: Abstract The chapter begins by quickly reviewing the background from general algebra which the reader is supposed to have throughout the book. After a discussion of ideal topologies on rings we develop the Krull–Remak–Schmidt theory of decompositions of modules into indecomposable constituents. It follows a treatment of idempotents in rings with an eye towards the decomposition of module categories into so-called blocks. Finally we discuss projective modules and introduce the Grothendieck groups of various classes of modules.

Keywords: Grothendieck Group; Identical Topology; Left Artinian; Isomorphism Classes; Left Noetherian (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-1-4471-4832-6_1

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