Question

let R and S be rings with identity. what are the units in the ring R x S

Answer 1

why isn't it just the units of R in the first slot and units of S in the second?

Answer 2

i.e. \(\{(r,s):\text{r is a unit of R, s is a unit of S}\}\)

Answer 3

the identity in \(RXS\) is \((1_R, 1_S)\) so this should work

Answer 4

I don't know, I didn't think it was that easy.

Answer 5

multiplication is given component wise, so i think it is right