Ring whose identity is $42$? I am looking to find an example of a ring, in which the identity is $42$.
My initial thoughts are, well would $\mathbb{Z}_{84}$ work?

How about the ring $R=\{0,42\}\subset\mathbb{Z}$ (subset as sets only, not a subring), where we define $0+x=x+0=x$, $0\cdot x=x\cdot0=0$, $42+42=0$, and $42\cdot42=42$? In other words, this is just $\mathbb{Z}_2$, but using "$42$" as the symbol for $\overline{1}$.
