Definition:Prime Subfield
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Definition
Let $F$ be a field.
From Intersection of Subfields is Subfield, the intersection of all the subfields of $F$ is itself a subfield which is unique and minimal.
This unique minimal subfield in a field $F$ is called the prime subfield of $F$.
Sources
- 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 2$. Elementary Properties
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $24$. The Division Algorithm
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 61.3$ Characteristic of an integral domain or field