Abstract
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.
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References
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S. Lang, Units and class groups in number theory and algebraic geometry, Bull. AMS Vol. 6 No. 3 (1982), pp. 253–316
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Lang, S. (2002). Modules. In: Algebra. Graduate Texts in Mathematics, vol 211. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0041-0_3
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DOI: https://doi.org/10.1007/978-1-4613-0041-0_3
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