Why is $\mathbb{Q}$ the minimal field that contains $0$ and $1$ ?
95937
Why aren't all prime subfields equal to {0,1}?
3129
A commutative ring is a field iff the only ideals are $(0)$ and $(1)$
1914
General way to determine $\mathbb{Q}(\gamma) = \mathbb{Q}(\alpha,\beta)$ given $\alpha$ and $\beta$
53513
Why is it that in $\mathbb{F}_q \setminus 0$, there are exactly as many squares as non-squares?
109647
Ext$_R^n(Q,A)=0=$Tor$_n^R(Q,A)$ where $Q$ is the field of fractions of a domain $R$
128701
Are $\mathbb{Q}$ or $\mathbb{Z}$ flat modules?
27021
Show that $Q[\sqrt3]$ is a field
89473
Uniqueness of minimal polynomial: $f(x)$ divides $g(x)$
23641
Quotient ring of field is zero or itself.
81550
Linking two theorems: on algebraic closure and on minimal splitting field
26055
Multiplication by $0$ in a field
63280
Show that the set $\mathbb{Q}[\sqrt{2}] = \{a + b \sqrt{2} \mid a, b \in \mathbb{Q}\}$ is a field with the usual multiplication and addition.
55050
How to show that $\mathbb{Q}(i,\sqrt[4]{1+i} )$ is not contained in any cyclotomic extension of $\mathbb{Q}(i)$?
98256
Subfields of $\mathbb{Q}(\sqrt{2},\sqrt{3})$
42332
Existence of multiplicative inverse in field $\mathbb{Q}(\sqrt{d})$
26999
How is the degree of the minimal polynomial related to the degree of a field extension?
51687
Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?