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 Games".

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

Jun 5, 2019 · Subfields of finite fields Ask Question Asked 14 years, 3 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 …

Subfields of Rings Ask Question Asked 13 years, 1 month ago Modified 8 years, 4 months ago

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

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...

These subfields correspond to distinct intermediate field extensions between $\mathbb {Q}$ and $\mathbb {Q} (\zeta_7)$ and are determined by the fixed elements under specific subgroups of the …

Dec 12, 2014 · The product of two fields is not a field, as it is not even an integral domain (as pointed out in a comment). But also, yes, a subfield has to contain the multiplicative identity of the original field …

Dec 1, 2020 · Field extensions and subfields Ask Question Asked 5 years, 3 months ago Modified 5 years, 3 months ago