finitely generated left module

finitely generated left module

[¦fī‚nīt·lē ‚jen·ə‚rād·əd ¦left ′mäj·əl]
(mathematics)
A left module over a ring A that has a finite subset, x1, x2, …, xn, such that any member of the module has the form a1 x1 t ⋯ t anxn, where a1, …, an are members of A.