Let $I$ and $J$ be ideals of a commutative ring $R$ such that $I + J = R$. Show that there is an ideal $K$ in $R$ with $R/K \cong R/I \times R/J$
1425
The Chinese Remainder Theorem for Rings.
24259
Quotient ring of $T/I$
92822
Finite number of elements generating the unit ideal of a commutative ring
98765
Showing that $G/(H\cap K)\cong (G/H)\times (G/K)$
89702
Let $R$ be a ring such that for all $a,b$ in $R$, $(a^2-a)b=b(a^2-a)$. Then $R$ is commutative
53266
Show that $R/I\otimes_R R/J\cong R/(I+J)$
16945
Finding the Ideals of a Direct Product of Rings
15320
Morita equivalence and right and left ideals of a Ring
90889
Prime ideals in a finite direct product of rings
70320
Let $R$ be a commutative Noetherian ring (with unity), and let $I$ be an ideal of $R$ such that $R/I \cong R$. Then is $I=(0)$?
3129
A commutative ring is a field iff the only ideals are $(0)$ and $(1)$
142863
Show that every ideal of the matrix ring $M_n(R)$ is of the form $M_n(I)$ where $I$ is an ideal of $R$
137450
Two-sided ideal generated by subset of not commutative ring
117786
Show that some monomial ideal is primary
88307
Commutative property of ring addition
39049
Ring With Unity As a Direct Sum of Non-Zero Ideals
69649
If an ideal contains the multiplicative identity, then it is the whole ring