Trivial (right or left) ideals of R imply that R is a division ring
29600
What is true for a ring with exactly two right ideals
75558
Counter-example for prime ideals in a non commutative ring.
28327
(Simple) Examples on Non-Commutative Rings
90889
Prime ideals in a finite direct product of rings
150986
For a Noetherian ring $R$, we have $\text{Ass}_R(S^{-1}M)=\text{Ass}_R(M)\cap \{P:P\cap S=\emptyset\}$
34203
if $S$ is a ring (possibly without identity) with no proper left ideals, then either $S^2=0$ or $S$ is a division ring.
111493
Division algorithm for polynomials in R[x], where R is a commutative ring with unity.
87151
Primary ideals in Noetherian rings
99567
Proving that an inverse ring homomorphism of an ideal is an ideal?
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
92822
Finite number of elements generating the unit ideal of a commutative ring
138309
Ring whose all ideals are double-sided is commutative?
65464
What are the left and right ideals of matrix ring? How about the two sided ideals?
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
137450
Two-sided ideal generated by subset of not commutative ring
98818
Quotient ring of a localization of a ring
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set