Algebra homomorphism
A homomorphism between two algebras, A and B, over a field (or ring) K, is a map F : A → B such that for all k in K and x, y in A,
If F is bijective then F is said to be an isomorphism between A and B.
A common abbreviation for "homomorphism between algebras" is "algebra homomorphism" or "algebra map". Every algebra homomorphism is a homomorphism of K-modules.
If A and B are two unital algebras, then an algebra homomorphism is said to be unital if it maps the unity of A to the unity of B. Often the words "algebra homomorphism" are actually used in the meaning of "unital algebra homomorphism", so non-unital algebra homomorphisms are excluded.
A unital algebra homomorphism is a ring homomorphism.
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