Algebra (ring Theory) - Associative Algebras

Associative Algebras

If A is a monoid under A-multiplication (it satisfies associativity and it has an identity), then the R-algebra is called an associative algebra. An associative algebra forms a ring over R and provides a generalization of a ring. An equivalent definition of an associative R-algebra is a ring homomorphism such that the image of f is contained in the center of A.