If you want interesting examples of finite fields and subfields, characteristic 2 offers Grundy numbers, otherwise known as Nimbers, whose arithmetic is explored in JH Conway "On Numbers and …

Jun 5, 2019 · Subfields of finite fields Ask Question Asked 14 years, 4 months ago Modified 6 years, 10 months ago

A non-algebraic example is $\mathbb {Q} (\pi)$. Using the axiom of choice, one can even construct "arbitrary complicated" subfields of $\mathbb {C}$. Generally speaking, many fields may be …

Feb 27, 2020 · Given $\mathbb {K}$ a field, what is the definition subfield of $\mathbb {K}$? Intuitively, I think a subfield as a subset of a field which itself is a field, in other words, satisfy the axioms that a

Possible Duplicate: Subfields of finite fields Field with $2^{15}$ elements How many subfields? Including trivial one and the whole thing I guess $15$. Right or not my guess? I think every sub...

Aug 3, 2015 · The relationship between subfields and subgroups of a finite field. Ask Question Asked 10 years, 8 months ago Modified 10 years, 8 months ago

Dec 1, 2020 · Field extensions and subfields Ask Question Asked 5 years, 4 months ago Modified 5 years, 4 months ago

Dec 7, 2023 · What are the proper subfields of the cyclotomic field extension generated by a primitive fifth root of unity? Ask Question Asked 2 years, 4 months ago Modified 11 months ago

Prove that the intersection of any family of subfields is itself a subfield. In the countable case: Suppose that $\mathscr K$ is a field and consider $ (\mathcal K_n)_ {n\in\mathbb N}\subset \maths...

Apr 21, 2021 · Quadratic subfields of the cyclotomic field $\mathbb {Q} (\zeta_ {14})$ Ask Question Asked 4 years, 11 months ago Modified 4 years, 9 months ago