Why the direct product does not form a ring?
69611
If $R$ and $S$ are rings then $R \times S$ is never a field
70610
Why is ring addition commutative?
42096
Direct product of Sylow subgroups
108601
Show structure of a commutative ring in a tensor product
26764
Proving that $\mathbb R^3$ cannot be made into a real division algebra (and that extending complex multiplication would not work)
29019
Ideals in direct product of rings
93343
Properties of rad A in rings.
125833
Semidirect Products with GAP
1751
When does the tensor product distribute over an infinite direct product?
141100
Nontrivial subring with unity different from the whole ring?
21992
Examples proving why the tensor product does not distribute over direct products.
153291
Why a ring homomorphism from a local ring will not map a non-unit to a unit？
42883
Cross product in $\mathbb R^n$
90889
Prime ideals in a finite direct product of rings
123860
When are two direct products of groups isomorphic?
144736
Why can't a string be formed by head String?
50114
A question about direct sums and products of modules