Composition of Homomorphisms/R-Algebraic Structure
From ProofWiki
Theorem
Let:
- $\left({S_1, *_1}\right)_R$
- $\left({S_2, *_2}\right)_R$
- $\left({S_3, *_3}\right)_R$
be $R$-algebraic structures with the same number of operations.
- $\phi: \left({S_1, *_1}\right)_R \to \left({S_2, *_2}\right)_R$
- $\psi: \left({S_2, *_2}\right)_R \to \left({S_3, *_3}\right)_R$
be homomorphisms.
Then the composite of $\phi$ and $\psi$ is also a homomorphism.
Proof
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Sources
- Seth Warner: Modern Algebra (1965): $\S 28$: Theorem $28.1$
