Equivalence of Definitions of Unital Associative Commutative Algebra/Homomorphisms
Jump to navigation
Jump to search
Definition
Let $A$ be a commutative ring with unity.
Let $\struct {B, f}$ and $\struct {C, g}$ be rings under $A$.
Let $h: B \to C$ be a mapping.
The following statements are equivalent:
- $(1): \quad h$ is a morphism of rings under $A$.
- $(2): \quad h$ is a unital algebra homomorphism from the algebra defined by $f$ to the algebra defined by $g$.
Proof
This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |