- #1
lostinmath08
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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
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?
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
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?