extended ideal
Let be a ring map. We can look at the ideal generated by the image of , which is called an extended ideal and is denoted by .
It is not true in general that if is an ideal in , the image of under will be an ideal in . (For example, consider the embedding . The image of the ideal is not an ideal in , since the only ideals in are and all of .)
Title | extended ideal |
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Canonical name | ExtendedIdeal |
Date of creation | 2013-03-22 12:55:34 |
Last modified on | 2013-03-22 12:55:34 |
Owner | drini (3) |
Last modified by | drini (3) |
Numerical id | 6 |
Author | drini (3) |
Entry type | Definition |
Classification | msc 13A15 |
Classification | msc 14K99 |
Related topic | ContractedIdeal |