Associative rings and algebras Chain, growth and finiteness conditions Concept
Classical ring of quotients
Summary
The classical ring of quotients of a ring is obtained by inverting all regular elements of . These are the elements that are not zero divisors on either side. It is the Ore localization of at the set of regular elements, when that localization exists. For an integral domain it is the field of fractions, and for a commutative ring it is the total ring of fractions. Goldie's theorem says exactly when this ring is semisimple Artinian.
Where this leads
2 pages build on this one.
Further reading
About this page
| Tag | C5971PGKPH |
|---|---|
| URI | m2://C5971PGKPH |
| Kind | concept |
| Writing | W0 stub |
| MSC | 16S85, 16U20, 16P60 |
| Specializes | Ore localization |
| Changed | 2 November 2026 |
Markdown · JSON · Edit on GitHub
What this page needs for W1
- an inventory row: the row of the inventory that the node accounts for (0 of 1)
- a source with a locator (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.