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## Tensor product of R-algebrasIn mathematics, there is a construction in abstract algebra of thetensor product of commutative rings; which puts a ring structure on the tensor product as abelian groups of two commutative rings R and S. This structure on R_{Z}S then makes it a coproduct in the category of commutative rings.
More generally, if R is a commutative ring and A and B are commutative R-algebras, we can make A .c'd = acbd, to have a well-defined product on A_{R}B; the ring axioms and R-linearity can be checked too.This construction is of constant use in algebraic geometry: working in the opposite category to that of commutative R-algebras, it provides pullbacks of affine schemes, otherwise known as fiber products. See also tensor product of fields. | |||||

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