In mathematics, a free module is a module that has a basis, that is, a generating set consisting of linearly independent elements. Wikipedia

In algebra, a module that has a basis Wikidata

A module that has a basis. Equivalently, a module consisting of n-tuples of ring elements with no extra identities. (Then the number n is said to be its rank.) Equivalently, a direct sum whose summands are all the same ring. (The quantity of summands may be more than two.). Wiktionary