# Definition:Subfield/Field

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

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## Definition

Let $\struct {F, +, \circ}$ be a field.

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

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

## Sources

- 1969: C.R.J. Clapham:
*Introduction to Abstract Algebra*... (previous) ... (next): Chapter $4$: Fields: $\S 16$. Subfields - 1971: Allan Clark:
*Elements of Abstract Algebra*... (previous) ... (next): Chapter $3$: Field Theory: Definition and Examples of Field Structure: $\S 88$ - 1978: Thomas A. Whitelaw:
*An Introduction to Abstract Algebra*... (previous) ... (next): $\S 56$. Subrings and Subfields: Definition $2$

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