Associative rings and algebras Modules and ideals Concept
Invariant basis number
Summary
A ring has invariant basis number (IBN) if any two bases of a finitely generated free module over it have the same size. For such a ring the rank of a free module is well defined, just as the dimension of a vector space is. All nonzero commutative rings and all division rings have this property, but some noncommutative rings do not.
Further reading
About this page
| Tag | AG1GMQDTDW |
|---|---|
| URI | m2://AG1GMQDTDW |
| Kind | concept |
| Writing | W0 stub |
| MSC | 16D40, 16E20 |
| Same as |
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