Solution Found!
Let R be a ring. The center of R is the set {x R
Chapter 12, Problem 19E(choose chapter or problem)
Let R be a ring. The center of R is the set {x ? R | ax = xa for all a in R}. Prove that the center of a ring is a subring.
Questions & Answers
QUESTION:
Let R be a ring. The center of R is the set {x ? R | ax = xa for all a in R}. Prove that the center of a ring is a subring.
ANSWER:Step 1 of 3
A ring R is a set with two binary operations, addition and multiplication, satisfying several properties: R is an Abelian group under addition, and the multiplication operation satisfies the associative law.
And distributive laws
For every
The identity of the addition operation is denoted as 0. If the multiplication operation has an identity. It is called a unity. If multiplication is commutative, we say that R is commutative.
A subring of a ring R is a subset
That is a ring under the operations of R.