## Mathematics, Department of

#### Date of this Version

12-1964

#### Abstract

The following is another short proof of the fact that for a commutative ring with unit *R*, any finitely based *R*-module is "dimensional" in the sense that all of its bases have the same number of elements.

THEOREM. *Let R be a commutative ring with unit. If M is a unitary R-module with a basis of n elements, then all bases of M contain exactly n elements.*

## Comments

Published in

The American Mathematical Monthly,Vol. 71, No. 10 (Dec., 1964), pp. 1112-1113 Copyright 1964 Mathematical Association of America Used by permission.