Let is not an ideal of R. (Hence, in Exercise 7 in Chapter
Chapter 14, Problem 31SE(choose chapter or problem)
Let
\(R=\left\{\left[\begin{array}{ll} a & b \\ c & d \end{array}\right] \mid a, b, c, d \in Z_{2}\right\} \)
with ordinary matrix addition and multiplication modulo 2. Show that
\(A=\left\{\left[\begin{array}{ll} 1 & 0 \\ 0 & 0 \end{array}\right] r \mid r \in R\right\} \)
is not an ideal of R. (Hence, in Exercise 7 in Chapter 14, the commutativity assumption is necessary.)
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