Two Ring is Boolean Ring
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Let $2$ be the two ring.
Then $2$ is a Boolean ring.
From Ring of Integers Modulo m is Ring, $2$ is a ring with unity.
Furthermore, the identities:
- $0 \cdot 0 = 0$
- $1 \cdot 1 = 1$
show that $2$ is also an idempotent ring.
Hence the result, by definition of Boolean ring.
- 2008: Paul Halmos and Steven Givant: Introduction to Boolean Algebras ... (previous) ... (next): $\S 1$