In the context of algebra, particularly in module theory, a **free module** is a specific type of module that is analogous to a free vector space. More formally, a module \( M \) over a ring \( R \) is called a free module if it has a basis, which is a set of elements in \( M \) that are linearly independent and can generate the entire module.
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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.