Field extension

In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field that contains the base field and satisfies additional properties. For instance, the set Q(√2) = {a + b√2 | a, b ∈ Q} is the smallest extension of Q that includes every real solution to the equation x = 2.

单词	Purely transcendental extension
释义	Purely transcendental extension 英语百科 Field extension In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field that contains the base field and satisfies additional properties. For instance, the set Q(√2) = {a + b√2 \| a, b ∈ Q} is the smallest extension of Q that includes every real solution to the equation x = 2.
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Purely transcendental extension

Field extension