If I define $ I.J=\{ij : i \in I $ & $ j \in J \} $. Then prove that it is not necessrily an ideal, where $I,J$ are ideals in a ring $R$.
124611
Which of the following is also an ideal?
63171
Translate of an ideal by $a$ coincides with the ideal iff  $a \in I$
587
Ideal Generated by the Union of Two Ideals
87078
Prove the following set is an ideal of the ring $Z[x]$
73417
$Rad(I)$ is an ideal of $R$
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
157605
$IS \mid JS$ implies that $I\mid J$ where $I$ and $J$ are ideals of a number ring contained in another number ring $S$
63338
Noncommutative failure of IBN: $\,R^n\cong R^m \Rightarrow n - m,$ ring $R$ with maximal ideal $I$ such that $R/I$ is not a division ring?
53770
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
21604
A complete ring with respect to an ideal
69352
Prove that $I= \{a+bi \in ℤ[i] : a≡b \pmod{2}\}$ is an maximal ideal of $ℤ[i]$.
138168
Prove: The pre-image of an ideal is an ideal.
41629
Structure of ideals in the product of two rings
156910
Necessary and sufficient condition for $R/IJ \cong R/I \times R/J$
52966
Rings, ideals and units-proof
99567
Proving that an inverse ring homomorphism of an ideal is an ideal?
118306
$I:=\{f(x)\in R\mid f(1)=0\}$ is a maximal ideal?