Let R be a commutative ring, and I, J denote two ideals in R such that I + J = R. Is it true that IJ = I ∩ J?
37393
$R$ is commutative, $I$,$J$ are ideals, $I+J=R$, then $IJ=I\cap J$
99567
Proving that an inverse ring homomorphism of an ideal is an ideal?
65224
Prove that if $a^2 = a$ for all elements of the ring $R$, then $R$ has characteristic 2. Is the converse of the statement true?
21604
A complete ring with respect to an ideal
17895
Let $R$ be a commutative ring with 1 then why does $a\in N(R) \Rightarrow 1+a\in U(R)$?
30714
A question on ring homomorphisms and maximal ideals.
150309
Why do we assume $a+b=b+a$ in a Ring with 1. Also, is it true with Rings without 1?
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 $k$
106894
If a subring of a ring R has identity, does R also have the identity?
60223
Two principal ideals coincide if and only if their generators are associated
119067
Basic Ring Theory Question involving the unit element
50445
Explaining the product of two ideals
69649
If an ideal contains the multiplicative identity, then it is the whole ring
115920
Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal
18971
Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$
131671
Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
74559
$A$ and $B$ are ideals of a ring ${R}$ such that $A\cap B=\{0\}$. Prove that $st=0$ for every $s\in A, t\in B$.