Uniqueness of Rank of Free Modules Over Commutative Rings
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Revision as of 21:41, 9 March 2023 by Kfagerstrom (talk | contribs) (Created page with "Let <math>R</math> be a commutative ring with <math>1 \ne 0</math> and let M be a free R-module. If A and B are both bases for M, then A and B have the same cardinality, meani...")
Let \(R\) be a commutative ring with \(1 \ne 0\) and let M be a free R-module. If A and B are both bases for M, then A and B have the same cardinality, meaning that there exists a bijection \(A → B\).
