this U is commutative, if a, b, c \(\in\) C(s) then ab U ac = ab + (ab)^c \cdot ac = ab + (a^c + b^c) \cdot ac = ab + (a^c + ab^c) \cdot ac = ab + a^c ac + ab^c ac = ab + a^2bc = ab + ab^c c = a \cdot (b + b^c c) = a \cdot (b U c) ba U ca = ????
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