Associative rings and algebras Modules and ideals Concept
Stably finite ring
Summary
A ring is stably finite when all its matrix rings are Dedekind-finite. Being Dedekind-finite does not pass to matrix rings in general, so this is a stronger condition. Stably finite nonzero rings have invariant basis number, so the rank of a finitely generated free module over them is well defined.
Further reading
About this page
| Tag | 7VRY94A22R |
|---|---|
| URI | m2://7VRY94A22R |
| Kind | concept |
| Writing | W0 stub |
| MSC | 16U99, 16D40 |
| Specializes | Dedekind-finite ring |
| Changed | 2 November 2026 |
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