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A free module has a basis: every element has a unique finite linear combination in that basis with coefficients in the scalar ring.
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Basis of a module
Free module
32
Universal property of a free module
Free module
29
Rank of a free module
Free module
23
Invariant basis number for a commutative ring
Free module
29
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Module theory
Commutative algebra
Algebra
Area of mathematics
Mathematics
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