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algebraic number field

In mathematics, an algebraic number field (or simply number field) is an extension field ${\\displaystyle K}$ of the field of rational numbers ${\\displaystyle \\mathbb {Q} }$ such that the field extension ${\\displaystyle K/\\mathbb {Q} }$ has finite degree (and hence is an algebraic field extension). Thus ${\\displaystyle K}$ is a field that contains ${\\displaystyle \\mathbb {Q} }$ and has finite dimension when considered as a vector space over ${\\displaystyle \\mathbb {Q} }$ .
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Algebraic_number_field)

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