Is $(\mathbb R^2,+,\cdot )$ a field where $(a,b)\cdot (c,d)=(ac-bd, ad+bc)$?
138911
Is $\mathbb R^2$ a field?
33233
Need to prove that $(S,\cdot)$ defined by the binary operation $a\cdot b = a+b+ab$ is an abelian group on $S = \Bbb R \setminus \{-1\}$.
46565
Show that $\mathbb{Q}(\sqrt{2})$ is a field.
77854
Which cyclotomic fields are different?
38489
Degree of the extension $\mathbb{Q}(\sqrt{a+\sqrt{b}})$ over $\mathbb{Q}$
55673
Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?
66313
$\mathbb{Z}[i]/(a+bi) \cong \mathbb{Z}_{a^2+b^2}$ if $(a,b)=1$
5996
Are $(\mathbb{R},+)$ and $(\mathbb{C},+)$ isomorphic as additive groups?
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
35777
$\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$
124564
Prove the ring $a+b\sqrt[3]{2}+c\sqrt[3]{4}$ has inverse and is a field
42883
Cross product in $\mathbb R^n$
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
92518
mod Distributive Law, factoring $\!\!\bmod\!\!:$ $\ ab\bmod ac = a(b\bmod c)$
145140
Subfield of $\mathbb{Q}(\sqrt[n]{a})$
127198
What is $\mathbb{C}^{Aut(\mathbb{C}/\mathbb{Q})}$?
142470
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})= \mathbb{Q}(\sqrt{p}\cdot \sqrt[3]{q})$ ??