Why can't $\mathbb{R}^3$ have an associative division algebra?
26764
Proving that $\mathbb R^3$ cannot be made into a real division algebra (and that extending complex multiplication would not work)
131319
I understand what a division ring is, but cannot find any examples. Can anyone give me one?
156089
Why is the associative property valid for modular arithmetic?
52081
Why is not the ring $\mathbb{Z}[2\sqrt{2}]$ a unique factorization domain?
102383
Associativity of Cartesian Product
154959
Proof of associativity of GCD?
58532
If $M$ is an Artinian $R$-module then $R/\mbox{ann}(M)$ is an Artinian ring?
74663
Is $\mathbb{R}$ an algebraic extension of some proper subfield?
75520
If $a^3 =a$ for all $a$ in a ring $R$, then $R$ is commutative.
82637
Does there exist a non-trivial, associative Lie algebra?
66866
Algebraic dual of $\mathbb{R}^{\mathbb{N}}$
39114
Prove that a set in $\mathbb R^3$ is not an algebraic set
128428
Why is the set of commutators not a subgroup?
24139
Logical explanation why exponentiation operation is not commutative and associative
4923
Why don't we study algebraic objects with more than two operations?
126331
Associative ring with identity, inverses, divisors of zero and Artinianity
79650
Division Rings and Division Algebras