Definition:Ring Monomorphism
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This page is about Ring Embedding. For other uses, see embedding.
Definition
Let $\struct {R, +, \circ}$ and $\struct {S, \oplus, *}$ be rings.
Let $\phi: R \to S$ be a (ring) homomorphism.
Then $\phi$ is a ring monomorphism if and only if $\phi$ is an injection.
Also known as
A monomorphism may also be referred to as an embedding.
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Also see
Linguistic Note
The word monomorphism comes from the Greek morphe (μορφή) meaning form or structure, with the prefix mono- meaning single.
Thus monomorphism means single (similar) structure.
Sources
- 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 3$. Homomorphisms
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $5$: Rings: $\S 24$. Homomorphisms
- 1970: B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra ... (previous) ... (next): $\S 2.2$: Homomorphisms: Definition $2.4$
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 57$. Ring homomorphisms: Remarks: $\text{(a)} \ (1)$