Prove these two elements are not associated in $\mathbb Q[x,y,z]/(x-xyz)$
10908
Associated elements in a ring
86015
$\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
137029
Prove that $\operatorname{Hom}_{\Bbb{Z}}(\Bbb{Q},\Bbb{Z}) = 0$ and show that $\Bbb{Q}$ is not a projective $\Bbb{Z}$-module.
96071
How to show that a prime ideal of height 2 can’t necessarily be generated by 2 elements? (Hartshorne exercise I.1.11)
139841
Proving $A\setminus(B\setminus C)$ is not equal to $(A\setminus B)\setminus C$
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
71361
Prove that $x^x+y^y=z^z$ doesn't have integer solutions
119052
Finding invertible elements in $\mathbb{Z}/m\mathbb{Z}$
48480
Find two elements that don't have a gcd in a subring of Gaussian integers
87682
Show that $\sqrt{2}\notin \mathbb{Q}(\sqrt[4]{3})$
67796
How to prove that the algebra $k[x, xy, xy^2, xy^3, \dotsc]$ is not finitely generated?
123458
Prove $( \lnot C \implies \lnot B) \implies (B \implies C)$ without the Deduction Theorem
78873
How to show that the monomials are not a Schauder basis for $C[0,1]$
42213
Computing $\text{Gal}(\mathbb{Q}^{ab}/\mathbb{Q})$
58329
Show that $y_1$ and $y_2$ are not Linearly Independent
125604
Proof that $\mathbb{Z}$ has no zero divisors
94747
Show that the rings $2\mathbb{Z}$ and $3\mathbb{Z}$ are not isomorphic.