Although this chapter is logically self-contained and prepares for future topics, in practice readers will have had some acquaintance with vector spaces over a field. We generalize this notion here to modules over rings. It is a standard fact (to be reproved) that a vector space has a basis, but for modules this is not always the case. Sometimes they do; most often they do not. We shall look into cases where they do.
KeywordsFiltration Prefix Verse Veri
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- [CCFT.91]_P. Cassou-Nogues, T. Chinburg, A. Frohlich, M. J. Taylor, L-functions and Galois modules, in L-functions and Arithmetic J. Coates and M.J. Taylor (eds.), Proceedings of the Durham Symposium July 1989, London Math, Soc. Lecture Note Series 153, Cambridge University Press (1991), pp. 75–139Google Scholar
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