Rings

• Nov 11th 2012, 10:05 PM
puneetha
Rings
Example of Subring is commutative whereas whole ring is not commutative??
• Nov 11th 2012, 10:10 PM
puneetha
Re: Rings
help me out plllllllllll
• Nov 11th 2012, 11:33 PM
Deveno
Re: Rings
sure.

let R = the ring of all 2x2 matrices with integer entries. this is clearly a non-commutative ring (for example, the matrices:

$A = \begin{bmatrix}1&0\\1&0 \end{bmatrix};\ B = \begin{bmatrix}1&1\\0&0 \end{bmatrix}$

do not commute).

but the matrices of the form:

$K = \begin{bmatrix}k&0\\0&k \end{bmatrix},\ k \in \mathbb{Z}$

form a sub-ring of R isomorphic to the integers, which is thus commutative.
• Nov 11th 2012, 11:53 PM
puneetha
Re: Rings
thank u sooooooo muchhhhhhhhh :) :)