Chapter 3, Rings
The set of odd integers is not a ring. We can also work with matrices whose elements come from any ring we know about, such as Mn(Zr). Example. Let R = M2(Z2). This is a nite (16 elements) noncommutative ring with identity 1R = 10 01 and zero element 0R = 00 00 . We give an example to show it is noncommutative: 10 00 01 00 = 01 00
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