Rank of a free module
= Rank of a free module
{title2=$\operatorname{rk}M$}
For a nonzero commutative scalar ring, every two bases of a finite-rank free module have the same cardinality. This cardinality is the rank.
= Rank of a free module
{title2=$\operatorname{rk}M$}
For a nonzero commutative scalar ring, every two bases of a finite-rank free module have the same cardinality. This cardinality is the rank.