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Finding the ideals of an algebra

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  1. Oct 16, 2015 #1
    Say I have the algebra [itex]\mathbb{Z}_5[x]/I [/itex] where is the [itex] I[/itex] is the principle ideal generated by [itex] x^2+4[/itex]. 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. jcsd
  3. Oct 16, 2015 #2
    anyone?
     
  4. Oct 16, 2015 #3

    HallsofIvy

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    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 [itex]A= Z_5 [x]/I[/itex]?

    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. [itex]Z_5[x][/itex] 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 [itex](x^2+ 4)Z_3[x][/itex] where [itex]Z_3[x][/itex] is the set of all polynomials of degree 3 or less with integer coefficients.
     
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