$J(F^n)=0$, where $F$ is an algebraically closed field
124460
Show that if $f \in \mathbb{C} \left[x_1, \dots, x_n \right]$ vanishes at every point of $\mathbb{Z}^n$, then $f$ is the zero polynomial.
81550
Linking two theorems: on algebraic closure and on minimal splitting field
117777
What are the zero divisors of $C[0,1]$?
127002
Prove that for a nonzero element $a$ of a field $F$ with $q$ elements $a^{-1} = a^{q-2}$
78143
Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements
149634
$ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$
95105
Solutions in complex number field, instead of $\mathbb{N}$, to Fermat's Last Theorem
113742
Nullstellensatz non-valid for non-algebraically closed fields
65619
Does $f^{(n)} = 0$ imply that complex $f$ is a polynomial?
15137
Does $IJ=IK\implies J=K$ always hold for integral domain and finitely generated nonzero ideal $I$?
48093
Irreducible polynomial in field extension
122050
Algebraic extension of perfect field in which every polynomial has a root is algebraically closed
96355
What is the first order axiom characterizing a field having characteristic zero?
82576
Intersection of two subfields of the Rational Function Field in characteristic $0$
19511
Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?
112556
When is $F(\sqrt c)$ a field?
139499
The algebraic closure of a finite field and its Galois group