noun
free module
In abstract algebra, a module that has a basis, i.e., a linearly independent generating set. This is the module-theoretic analogue of a vector space.
整数環上の自由加群は、階数が一意に定まる。
A free module over the ring of integers has a uniquely determined rank.
すべてのベクトル空間は、体上の自由加群と見なせる。
Every vector space can be regarded as a free module over a field.
Compound of 自由 (free) + 加群 (module), a calque of the English mathematical term 'free module'.