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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
  • Mathematics

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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