total ring of fractions
For a commutative ring having regular elements, we may form , the total ring of fractions
(quotients) of , as the localization
of at , where is the set of all non-zero-divisors of . Then, can be regarded as an extension ring of (similarly as the field of fractions
of an integral domain
is an extension ring). has the non-zero unity 1.
| Title | total ring of fractions |
|---|---|
| Canonical name | TotalRingOfFractions |
| Date of creation | 2013-03-22 14:22:31 |
| Last modified on | 2013-03-22 14:22:31 |
| Owner | pahio (2872) |
| Last modified by | pahio (2872) |
| Numerical id | 13 |
| Author | pahio (2872) |
| Entry type | Definition |
| Classification | msc 13B30 |
| Synonym | total ring of quotients |
| Related topic | ExtensionByLocalization |
| Related topic | FractionField |