R is a quasi-semi-local ring, I is ideal of R. Prove Jac(R/I)=(JacR + I)/I
112666
Image of Jacobson Radical is the Jacobson Radical
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 $R$
102316
why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$
57031
Ring of fractions of $R$ is integral over $R$
74559
$A$ and $B$ are ideals of a ring ${R}$ such that $A\cap B=\{0\}$. Prove that $st=0$ for every $s\in A, t\in B$.
138752
Prove the Radical of an Ideal is an Ideal
114343
If $I$ and $J$ are ideals in a ring $R$ with $1$ such that $I+J = R$, show that $I^m$ and $J^n$ are co-maximal for all $m,n \in \mathbb{N}$
124646
Understanding the ideal $IJ$ in $R$
157488
Proving that $k[x,y,z]/(xz - (y^2 + 1))$ is a normal ring.
151803
Prove that $R$ is commutative
157605
$IS \mid JS$ implies that $I\mid J$ where $I$ and $J$ are ideals of a number ring contained in another number ring $S$
133706
If R is a local ring, then its maximal left-ideal is a left and right ideal
19112
Ring $R= \mathbb Z_3[x]/\langle x^6-1\rangle$
79535
Prove that $R$ is a commutative ring if $x^3=x$
56278
$I$ and $J$ are coprime ideals iff $x \to (x + I, x + J)$ is surjective.
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
42871
Quotient of a local regular ring