Let R be a ring and A,B,C ideals such that A+B=R and BC $\subset$ A , then C $\subset$ A
236
Proof of general Euclid's Lemma in a UFD (by Euclidean algorithm?)
148208
In Noetherian ring $R$, ideal $I\subset R$, $P\in\mathrm{Ass}(I),P=I:a$ for some $a\in R$.
117590
Let I and J be ideals of a ring R. Show by example that the set of products {xy | x ∈ I, y ∈ J} need not be an ideal
131671
Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
37410
Example of a ring with an infinite inclusion chain of ideals
118781
product of ideals in matrix ring
133706
If R is a local ring, then its maximal left-ideal is a left and right ideal
58640
$R$ is an algebra over an infinite field. If $\exists$ ideals s.t. $J\subseteq \bigcup_{k=1}^nI_k$ then $J\subseteq I_k$ for some $k$
41080
If A, B, and C are set and $A \subset B ,B \subset C \rightarrow A \subset C$
8787
In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
60223
Two principal ideals coincide if and only if their generators are associated
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
135699
Questions about a commutative ring with exactly three ideals
82003
Bijection between sets of ideals
47856
$f(x)=ax+b$ for some $a,b\in\mathbb{Q}$ if $f(\mathbb{Q})\subset\mathbb{Q}$ and $f(\mathbb{R-Q})\subseteq \mathbb{R}-\mathbb{Q}$
116883
About ideals in a ring which is a $k$ vector space
149519
Prove that a Boolean ring is a Bezout ring .