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Homework Statement
Let A be the algebra [itex]\mathbb{Z}_5[x]/I[/itex] where [itex]I[/itex] is the principle ideal generated by [itex]x^2+4[/itex] and [itex]\mathbb{Z}_5[x][/itex] is the ring of polynomials modulo 5.
Find all the ideals of A
Let G be the group of invertible elements in A. Find the subgroups of the prime decomposition.
Homework Equations
None
The Attempt at a Solution
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I have no idea where to start. Why is [itex]x^2+4[/itex] an ideal? How do I find other ideals?
I have been asked about invertible elements in rings like [itex]\mathbb{Z}/n\mathbb{Z}[/itex] (just the elements co-prime to n) but how does this concepts relate to polynomials? Are invertible elements in polynomial rings also "coprime" in some sense??
Thankyou
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