Question

If ( R ,*1,*2) is a ring, then ψ : R × R → R :ψ(r1,r2) = r1 *2 r1 is a binary operation. State whether the given statement is true or false , justify with reason.

Answer 1

Answer on Question #80553 – Math – Abstract Algebra

Question

If $(R, *1, *2)$ is a ring, then $\psi : R \times R \to R : \psi(r1, r2) = r1 * 2r1$ is a binary operation. State whether the given statement is true or false, justify with reason.

Solution

For all $r_1 \in R$ $r_1 *_{2} r_1 \in R$, then $\psi: R \times R \to R$. Hence $\psi$ is a binary operation.

Answer: True.

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