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R-algebra)
In ring theory, an algebra over a base ring is a generalization of the concept of associative algebra.
Let R be a commutative ring and let S be another ring (not necessarily commutative). S is called an R-algebra if there is a ring homomorphism from R into the center of S. If S itself is commutative it is called a commutative R-algebra.
The notion of R-algebra generalizes that of an associative algebra: if k is a field, then any associative algebra over k is a k-algebra.
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