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About: Free product of associative algebras     Goto   Sponge   NotDistinct   Permalink

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In algebra, the free product (coproduct) of a family of associative algebras over a commutative ring R is the associative algebra over R that is, roughly, defined by the generators and the relations of the 's. The free product of two algebras A, B is denoted by A ∗ B. The notion is a ring-theoretic analog of a free product of groups. In the category of commutative R-algebras, the free product of two algebras (in that category) is their tensor product.