Abstract Algebra/Algebras

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Let R be a ring. An R-algebra is a pair (f,\,S) where f\; \colon\; R\;\to\; S is a ring homomorphism. By convention, if R is a commutative ring with multiplicative identity, then f should preserve that identity. An R-algebra homomorphism h\;:\;(f,\,S)\; \to\; (g,\,T) is a ring homomorphism so that g\circ h=f.

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