Solution Found!
Let Prove or disprove that the mapping is a ring
Chapter 15, Problem 16E(choose chapter or problem)
QUESTION:
Let \(R=\left\{\left[\begin{array}{ll}a & b \\ 0 & c\end{array}\right] \mid a, b, c \in Z\right\}\). Prove or disprove that the mapping \(\left[\begin{array}{ll}a & b \\ 0 & c\end{array}\right] \rightarrow a\) is a ring homomorphism.
Questions & Answers
QUESTION:
Let \(R=\left\{\left[\begin{array}{ll}a & b \\ 0 & c\end{array}\right] \mid a, b, c \in Z\right\}\). Prove or disprove that the mapping \(\left[\begin{array}{ll}a & b \\ 0 & c\end{array}\right] \rightarrow a\) is a ring homomorphism.
ANSWER:Step 1 of 3
We denote given mapping with . It is obviously additive, so we only need to verify that preserves multiplication.