$M=I\times J $ for some $I,J$
29019
Ideals in direct product of rings
35777
$\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$
139833
Prove that $\gcd(M, N)\times \mbox{lcm}(M, N) = M \times N$.
67772
How to find $k$ such that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_k$
53266
Show that $R/I\otimes_R R/J\cong R/(I+J)$
149553
Is it always true that $(A_1 \cup A_2) \times (B_1 \cup B_2)=(A_1\times B_1) \cup (A_2 \times B_2)$
106756
Union and Intersection of Sets $A_{i}$ and $B_{j}$
64747
If $A^m=I$ then A is Diagonalizable
64130
Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
87848
Formal proof for $(-1) \times (-1) = 1$
13026
Prove that if AB=I_m, then rk(A)=rk(B).
52564
$m\times n$ matrix with an even number of 1s in each row and column
64656
how do you prove that $A\times (B\setminus C) = (A\times B) \setminus (A\times C)$?
120094
Prove, that for any A, B, C sets, $A\times (B\setminus C) = (A\times B)\setminus (A\times C)$ is true.
53190
Is there an equivalent of $\pm$ but for $\times$ and $\div$?
123726
$2\times 2 $ matrices over $\mathbb{C}$ that satisfy $\mathrm A^3=\mathrm A$
87289
Find the multiplicative inverses of all the elements in $\Bbb Z_{16}^\times$