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 |
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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 |