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Question about ideal of a ring

by DukeSteve
Tags: abstract algebra, ideals, rings
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DukeSteve
#1
Mar12-11, 06:27 PM
P: 10
Hello Experts,

Again a Q and what I did, please tell me what I am doing wrong:

Given that there is a ring of matrices above Z (integers) Mn(Z) and 2 ideals I, J of this ring.

I need to prove that they are commutative: IJ = JI

What I did is that:

For all i in I and for all M in Mn(Z) n is the the size of a matrix n x n

M*i in I and i*M is also in I.

same with J : j*M in J and M*j is in J

For every k in J and for every h in I:

kh = j*M*i*M = j*(M*i)*M = .... I don't know what to do from here.... please guide me.
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gilsonrfilho
#2
Mar16-11, 07:51 PM
P: 1
Hey Duke!
I suggest you to check again your hypothesys instead.
Well, [tex]\mathbb{Z}[/tex] is a ring with unity, right? What's the form of it's ideals? What's the form of the ideals of [tex]M_{n}(\mathbb{Z})[/tex]?

The problem of your approach is that I can't really see a way to use your hypothesys.


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