extended ideal

Let f:AB be a ring map. We can look at the ideal generated by the image of 𝔞, which is called an extended ideal and is denoted by 𝔞e.

It is not true in general that if 𝔞 is an ideal in A, the image of 𝔞 under f will be an ideal in B. (For example, consider the embedding f:. The image of the ideal (2) is not an ideal in , since the only ideals in are {0} and all of .)

Title extended ideal
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