Show that the factor ring $R[x]/(1−ax)$ is a zero ring, that is, $R[x]/(1−ax)=\{(1−ax)\}$
17895
Let $R$ be a commutative ring with 1 then why does $a\in N(R) \Rightarrow 1+a\in U(R)$?
69728
If $f$ divides $g$ in $S[x]$, show that $f$ divides $g$ in $R[x]$ for $R$ a sub-ring of $S$.
31933
$x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
138826
To show that either $R$ is a field or $R$ is a finite ring with prime number of elements and $ab = 0$ for all $a,b \in R$.
95146
Polynomial ring $R[X] $ has zero Jacobson radical, for $R$ a domain
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 $R$
114254
Zero divisors in $A[x_1,x_2,\dots,x_r]$
32772
Proving units in a ring
26805
Non-Noetherian 0-dimensional ring
1141
Existence of totally ordered ring with zero divisors
133495
Example of a ring without Invariant Basis Property
129371
Maximal ideals in the ring of real functions on $[0,1]$
69353
Show that a ring with only trivial right ideals is either a division ring or $|R|=p$ and $R^2=\{0\}$. Why would $R$ be finite?
125604
Proof that $\mathbb{Z}$ has no zero divisors
126331
Associative ring with identity, inverses, divisors of zero and Artinianity
98818
Quotient ring of a localization of a ring
74441
Zero divisors in matrix rings