# Maximal sets of linearly independent vectors in a free module over a commutative ring

- Authors
- Journal
- Linear Algebra and its Applications 0024-3795
- Publisher
- Elsevier
- Publication Date
- Volume
- 168
- Identifiers
- DOI: 10.1016/0024-3795(92)90291-h
- Disciplines

## Abstract

Abstract The following theorem is proved: If R is a noetherian ring, M is a free R-module of rank n, and {v 1,…, v s } is the maximal set of linearly independent vectors, then always s= n. An example is also given of a commutative ring R for which the above theorem is false for every n⩾2.

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