Abstract
Since all bases for a vector space V have the same cardinality, the concept of vector space dimension is well-defined. A similar statement holds for free R-modules when the base ring is commutative (but not otherwise).
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© 2005 Steven Roman
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(2005). Modules II: Free and Noetherian Modules. In: Advanced Linear Algebra. Graduate Texts in Mathematics, vol 135. Springer, New York, NY. https://doi.org/10.1007/0-387-27474-X_6
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DOI: https://doi.org/10.1007/0-387-27474-X_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-24766-3
Online ISBN: 978-0-387-27474-4
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