integral
Let B be a ring with a subring A. We will assume that A is contained in the center of B (in particular, A is commutative). An element x∈B is integral over A if there exist elements a0,…,an-1∈A such that
xn+an-1xn-1+⋯+a1x+a0=0. |
The ring B is integral over A if every element of B is integral over A.
Title | integral |
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Canonical name | Integral |
Date of creation | 2013-03-22 12:07:44 |
Last modified on | 2013-03-22 12:07:44 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 9 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 13B21 |
Related topic | IntegralBasis |