Exchange Modules and Exchange Rings

Martin Mathieu
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Martin Mathieu: Queen’s University Belfast, School of Mathematics and Physics

Chapter 9 in Classically Semisimple Rings, 2022, pp 109-129 from Springer

Abstract: Abstract Our penultimate chapter is devoted to an extension of the concept of semisimple module and, as a consequence, the notion of a semisimple ring. The exchange property for modules was introduced by Crawley and Jónsson in 1964 and the concept of an exchange ring belongs to Warfield (1972). Our main sources for this chapter are Clark et al. (Lifting Modules; Supplements and Projectivity in Module Theory. Frontiers in Mathematics. Birkhäuser Verlag, Basel, 2006) and Facchini (Module Theory: Endomorphism Rings and Direct Sum Decompositions in Some Classes of Modules. Progress in Mathematics, vol. 167. Birkhäuser Verlag, Basel, 1998), which contain references to the original articles and a lot of additional information.

Date: 2022
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DOI: 10.1007/978-3-031-14209-3_9

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