Show that $R/ I=\{x+I\mid x\in R\}$ is a Ring if $I$ is an Ideal and it isn't if $I$ is only a subring
67260
What happens if we change the definition of quotient ring to the one that does not have ideal restriction?
154613
Showing a set of fractions is a ring
8787
In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
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 $R$
104789
How to tell an ideal of integer polynomial ring is principal?
157488
Proving that $k[x,y,z]/(xz - (y^2 + 1))$ is a normal ring.
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
138337
On a ring $R$ where $x^2 = x$, we must have that $2x = 0$ and $R$ is commutative
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
19112
Ring $R= \mathbb Z_3[x]/\langle x^6-1\rangle$
116883
About ideals in a ring which is a $k$ vector space
41629
Structure of ideals in the product of two rings
83100
Prove that the center of a ring is a subring.
77198
Showing that the characteristic of a commutative ring R without zero divisors is 0 or prime
119067
Basic Ring Theory Question involving the unit element
19838
Prove that in general the set of the right zero divisors is different from the set of left zero divisors in a ring R
137450
Two-sided ideal generated by subset of not commutative ring