(adsbygoogle = window.adsbygoogle || []).push({}); 1.The problem statement

Let R be a ring. The center of R is defines as follows:

Z(R)= {x E R where xy = yx for all y E R}

Show that Z(R) is a subring of R

3. The attempt at a solution

I know that rings have to follow 4 axioms

a) its an abelian group under addition

b) Closure (ab E R)

c) Associativity ((ab)c =a(bc)

d) Distributivity a(b+c)=ab+ac and (b+c)a= ba+ca

Do the axioms apply to sub rings as well? and how would u go about solving it?

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# The Center of a Ring and Subrings!

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