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Let $+,\cdot$ denote multiplication in $\mathbb{N}_0$. The addition and multiplication in $\operatorname{On}_p$ are denoted $\oplus, \otimes$. Recursive definition of addition: $$x \oplus y := ((x+y) \...

In an article, I've found the following result. Unfortunately, it was derived from a general, somewhat complicated theory, that would be cumbersome for this result alone. Assume that $\mathbb F_p$ is ...

Which fields $k$ have the property that any sum of squares is a square ? Are there elegant characterizations and/or classifications known for this type of field ? And what if we replace "fields" by "...

This question follows Field theory by Steven Roman, Chapter 9, Exercise 20. Denote the algebraic closure of the finite field $F_q$ by $\Gamma(q)$, and let $a_n$ be any strictly increasing infinite ...