Search results
Search: MSC category 13B25
( Polynomials over commutative rings [See also 11C08, 11T06, 13F20, 13M10] )
1. CMB Online first
 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 

2. 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 

3. 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 
