Associative rings and algebras Conditions on elements Concept
Clean ring
Summary
A clean ring is a ring in which every element is the sum of an idempotent and a unit. The notion was introduced by W. K. Nicholson in his study of exchange rings, and every clean ring is an exchange ring. Local rings, matrix rings over local rings and unit-regular rings are clean. Cleanness gives a supply of idempotents and units that helps in decomposing modules.
Further reading
About this page
| Tag | CYCTQ0CR3K |
|---|---|
| URI | m2://CYCTQ0CR3K |
| Kind | concept |
| Writing | W0 stub |
| MSC | 16U60, 16U40 |
| Same as | |
| Changed | 2 November 2026 |
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