# Definition:Subfield/Ring

< Definition:Subfield(Redirected from Definition:Subfield of Ring)

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## Definition

Let $\struct {R, +, \circ}$ be a ring with unity.

Let $K$ be a subset of $R$ such that $\struct {K, +, \circ}$ is a field.

Then $\struct {K, +, \circ}$ is a **subfield** of $\struct {R, +, \circ}$.

## Sources

- 1964: Iain T. Adamson:
*Introduction to Field Theory*... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 2$. Elementary Properties

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- 1972: A.G. Howson:
*A Handbook of Terms used in Algebra and Analysis*... (previous) ... (next): $\S 6$: Rings and fields