Register to reply

Question about ideal of a ring

by DukeSteve
Tags: abstract algebra, ideals, rings
Share this thread:
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.
Phys.Org News Partner Science news on
Scientists discover RNA modifications in some unexpected places
Scientists discover tropical tree microbiome in Panama
'Squid skin' metamaterials project yields vivid color display
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.

Register to reply

Related Discussions
Simple ring, maximal ideal Calculus & Beyond Homework 2
Ideal and Factor Ring Calculus & Beyond Homework 1
One question related to an ideal of Ring R General Math 1
Ideal and factor ring problem Calculus & Beyond Homework 1
Prime ideal in ring Calculus & Beyond Homework 0