1. CMB Online first
 Polak, Jason K. C.

Counting separable polynomials in $\mathbb{Z}/n[x]$
For a commutative ring $R$, a polynomial $f\in R[x]$ is called
separable if $R[x]/f$ is a separable $R$algebra. We derive formulae
for the number of separable polynomials when $R = \mathbb{Z}/n$, extending
a result of L. Carlitz. For instance, we show that the number
of separable polynomials in $\mathbb{Z}/n[x]$
that are separable is $\phi(n)n^d\prod_i(1p_i^{d})$
where $n = \prod p_i^{k_i}$ is the prime factorisation of $n$
and $\phi$ is Euler's totient function.
Keywords:separable algebra, separable polynomial Categories:13H05, 13B25, 13M10 

2. CMB 2016 (vol 59 pp. 794)
 Hashemi, Ebrahim; Amirjan, R.

Zerodivisor Graphs of Ore Extensions over Reversible Rings
Let $R$ be an associative ring with identity.
First we prove some results about zerodivisor graphs of reversible
rings. Then we study the zerodivisors of the skew power series
ring $R[[x;\alpha]]$, whenever $R$ is reversible and $\alpha$compatible. Moreover, we compare the diameter and girth of the zerodivisor
graphs of $\Gamma(R)$, $\Gamma(R[x;\alpha,\delta])$ and $\Gamma(R[[x;\alpha]])$,
when
$R$ is reversible and $(\alpha,\delta)$compatible.
Keywords:zerodivisor graphs, reversible rings, McCoy rings, polynomial rings, power series rings Categories:13B25, 05C12, 16S36 

3. CMB 2000 (vol 43 pp. 312)
 Dobbs, David E.

On the Prime Ideals in a Commutative Ring
If $n$ and $m$ are positive integers, necessary and sufficient
conditions are given for the existence of a finite commutative ring $R$
with exactly $n$ elements and exactly $m$ prime ideals. Next,
assuming the Axiom of Choice, it is proved that if $R$ is a
commutative ring and $T$ is a commutative $R$algebra which is
generated by a set $I$, then each chain of prime ideals of $T$ lying
over the same prime ideal of $R$ has at most $2^{I}$ elements. A
polynomial ring example shows that the preceding result is
bestpossible.
Categories:13C15, 13B25, 04A10, 14A05, 13M05 

4. CMB 1999 (vol 42 pp. 231)
 Rush, David E.

Generating Ideals in Rings of IntegerValued Polynomials
Let $R$ be a onedimensional locally analytically irreducible
Noetherian domain with finite residue fields. In this note it is
shown that if $I$ is a finitely generated ideal of the ring
$\Int(R)$ of integervalued polynomials such that for each $x \in
R$ the ideal $I(x) =\{f(x) \mid f \in I\}$ is strongly
$n$generated, $n \geq 2$, then $I$ is $n$generated, and some
variations of this result.
Categories:13B25, 13F20, 13F05 
