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The free \(A\)-ring is a graded \(A\)-ring. (English) Zbl 0791.16021

Let \(K\) be a commutative ring and \(A\) a \(K\)-algebra. The author defines the tensor \(A\)-ring on a set \(X: A_ K\langle X\rangle\) which he calls the free \(A\)-ring, proves the expected universal property and shows that it is graded as an \(A\)-ring. (In addition to one source referred to in the text, the bibliography contains 31 items, none dated after 1969).
Reviewer: P.M.Cohn (London)

MSC:

16S10 Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
16W50 Graded rings and modules (associative rings and algebras)
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