1. CMB Online first
||Zero-divisor graphs of Ore extensions over reversible rings|
Let $R$ be an associative ring with identity.
First we prove some results about zero-divisor graphs of reversible
rings. Then we study the zero-divisors 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 zero-divisor
graphs of $\Gamma(R)$, $\Gamma(R[x;\alpha,\delta])$ and $\Gamma(R[[x;\alpha]])$,
$R$ is reversible and $(\alpha,\delta)$-compatible.
Keywords:zero-divisor graphs, reversible rings, McCoy rings, polynomial rings, power series rings
Categories:13B25, 05C12, 16S36
2. CMB 2016 (vol 59 pp. 340)
||A Note on Algebras that are Sums of Two Subalgebras|
We study an associative algebra $A$ over an arbitrary field,
a sum of two subalgebras $B$ and $C$ (i.e. $A=B+C$). We show
that if $B$ is a right or left Artinian $PI$ algebra and $C$
is a $PI$ algebra, then $A$ is a $PI$ algebra. Additionally we
generalize this result for semiprime algebras $A$.
Consider the class of
all semisimple finite dimensional algebras $A=B+C$ for some
subalgebras $B$ and $C$ which satisfy given polynomial identities
$f=0$ and $g=0$, respectively.
We prove that all algebras in this class satisfy a common polynomial
Keywords:rings with polynomial identities, prime rings
Categories:16N40, 16R10, , 16S36, 16W60, 16R20
3. CMB 2014 (vol 57 pp. 609)
||Jacobson Radicals of Skew Polynomial Rings of Derivation Type|
We provide necessary and sufficient conditions for a skew polynomial ring of derivation type to be semiprimitive, when the base ring has no nonzero nil ideals. This extends existing results on the Jacobson radical of skew polynomial rings of derivation
Keywords:skew polynomial rings, Jacobson radical, derivation
4. CMB 1999 (vol 42 pp. 298)