Abstract Algebra: Theory and Applications · Problem 32

Polynomials — Thomas Judson

Mathematics — Abstract Algebra · center-of-a-ring

Problem

Let RR be a ring. Define the center of RR to be Z(R)={a∈R:ar=ra for all r∈R}.Z(R) = \{a \in R : ar = ra \text{ for all } r \in R\}. Prove that Z(R)Z(R) is a commutative subring of RR.

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