overring
Let be a commutative ring having regular elements and let be the total ring of fractions of . Then . Every subring of containing is an overring of .
Example. Let be a rational prime number. The -integral rational numbers (http://planetmath.org/PAdicValuation) are the quotients of two integers such that the divisor (http://planetmath.org/Division) is not divisible by . The set of all -integral rationals is an overring of .
Title | overring |
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Canonical name | Overring |
Date of creation | 2013-03-22 14:22:33 |
Last modified on | 2013-03-22 14:22:33 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 12 |
Author | pahio (2872) |
Entry type | Definition |
Classification | msc 13B30 |
Related topic | AConditionOfAlgebraicExtension |