Let $R$ be a commutative ring. For $a \in R$ consider the set $(a) = \{r*a | r\in R\}$. Show that $(a) = R$ if a is a unit of $R$
50908
Showing a Ring and an Ideal are equal
148550
Units in quotient ring of $\mathbb Z[X]$
87078
Prove the following set is an ideal of the ring $Z[x]$
122958
$R/I$ is commutative iff $rs-sr \in I$
27766
Comaximal ideals in a commutative ring
18971
Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$
110984
Ideals and prime ideals in a commutative ring.
32772
Proving units in a ring
83009
Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field
155445
What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$?
99715
Proper ideal and units proof
19112
Ring $R= \mathbb Z_3[x]/\langle x^6-1\rangle$
30327
$\ker \phi = (x_1-a_1, ..., x_n-a_n)$ for a ring homomorphism $\phi: R[x_1, ..., x_n] \to R$
37393
$R$ is commutative, $I$,$J$ are ideals, $I+J=R$, then $IJ=I\cap J$
127418
If ring $B$ is integral over $A$, then an element of $A$ which is a unit in $B$ is also a unit in $A$.
80827
Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
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 $a,b \in R$.