$0 \times a \cong 0$ without exponentiation
54127
Categories with $C \times 0 \cong 0$ for all objects $C$
127664
Inverse elements in the absence of identities/associativity.
116501
How to show equinumerosity of  the powerset of $A$ and the set of functions from $A$ to $\{0,1\}$ without cardinal arithmetic?
150605
Existence of a regular uncountable $\aleph_{\alpha}$ without $\mathsf{AC}$
17926
Zero divisor in $R[x]$
132165
"Polynomials" with non-integer exponents
114254
Zero divisors in $A[x_1,x_2,\dots,x_r]$
46843
A ring without the Invariant Basis Number property
148569
Embeddings $A → B → A$, but $A \not\cong B$?
8746
Groups of order $pq$ without using Sylow theorems
62566
Does $X\times S^1\cong Y\times S^1$ imply that $X\times\mathbb R\cong Y\times\mathbb R$?
131905
Proof for exponentiation in modular arithmetic
44361
An automorphism that has no fixed points except for the identity and is its own inverse implies commutativity
117777
What are the zero divisors of $C[0,1]$?
31380
Exponent and abelian groups
139
Prove or disprove: For every integer a, if a is not congruent to 0 (mod 3), the a^2 is congruent to 1 (mod 3)
33735
The square of an integer is congruent to 0 or 1 mod 4