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This gives the impression that every ring R is an algebra over every commutative subring, which is false, take for example the quaternions as a ring and the complex numbers as a commutative subring. Maybe one should omit the word "so" and everything's fine? --
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is continuous, preserving products, pullbacks, the terminal object, and other limits, and I'd thought maybe the center of rings functor preserved colimits, but I'm not 100% sure that the coproduct of rings, the
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I don't think that one should write "The center is a commutative subring of R, so R is an algebra over its center."
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and an analogous quotient for rings (quotient out by the 2-sided ideal generated by all ring-theoretic commutators
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The center is not functorial, neither for groups nor for rings. The inclusion of {e, (1 2)} into
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