highjacking this dog spammed thread
rainlet here, R cross R is an R-algebra, being a cross product of (trivial) R algebras. It's clearly two dimensional. but this:
https://math.stackexchange.com/questions/2217906/what-are-the-three-non-isomorphic-2-dimensional-algebras-over-mathbbrshows that all 2d R algebras are either the complex numbers, the set A = {x + jy} where j^2 = 1 or B = {x + ey} where e^2 = 0. Which one of these is RxR then?
