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Yeah, and if you carefully expand 1+(A+B+C)+(A+B+C)^2+(A+B+C)^3+..., there'll be strictly more summands than in (1+A+A^2+A^3+...)×(1+B+B^2+B^3+...)×(1+C+C^2+C^3
by Joker_vD 3y ago
Yeah, and if you carefully expand 1+(A+B+C)+(A+B+C)^2+(A+B+C)^3+..., there'll be strictly more summands than in (1+A+A^2+A^3+...)×(1+B+B^2+B^3+...)×(1+C+C^2+C^3+...) due to more flexible ordering of elements, so they're not isomorphic.
I still think it's the most obvious thing that [A+B+C] at least maps surjectively onto [A]×[B]×[C] :)