# Finding the ideals of an algebra

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1. Oct 16, 2015

### DeldotB

Say I have the algebra $\mathbb{Z}_5[x]/I$ where is the $I$ is the principle ideal generated by $x^2+4$. How do I find the ideals in A? I cant seem to find an explanation that is clear anywhere. Thanks!

Last edited: Oct 16, 2015
2. Oct 16, 2015

### DeldotB

anyone?

3. Oct 16, 2015

### HallsofIvy

I am a bit confused by your "How do I find the ideals in A?" when there is no mention of A! Did you mean $A= Z_5 [x]/I$?

A subset, S, of an algebra, A, is an "ideal" if and only if the product of a member of s with any member of A is again in S. $Z_5[x]$ is the set of all polynomials of degree 5 or less with integer coefficients. I is the set of all such polynomials of the form $(x^2+ 4)Z_3[x]$ where $Z_3[x]$ is the set of all polynomials of degree 3 or less with integer coefficients.