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Anonymous at Tue, 18 Jun 2024 03:10:45 UTC No. 16240464
Brainlet 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/ques
shows 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?
Anonymous at Tue, 18 Jun 2024 05:33:56 UTC No. 16240585
>>16240464
A
it's literally written in the response to the question
{x+iy:x,y∈R,i2=1}≅R[x]/(x2−1)≅R[x]/
Anonymous at Tue, 18 Jun 2024 06:13:50 UTC No. 16240615
https://en.m.wikipedia.org/wiki/Spl
The isomorphism is stated right at the top of the article. All you need to understand is that the multiplicative unit in RxR is (1,1) which obviously has more than one "root".