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Search: MSC category 16S36 ( Ordinary and skew polynomial rings and semigroup rings [See also 20M25] )

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1. CMB Online first

Kȩpczyk, Marek
A note on algebras that are sums of two subalgebras
We study an associative algebra $A$ over an arbitrary field, that is 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 identity.

Keywords:rings with polynomial identities, prime rings
Categories:16N40, 16R10, , 16S36, 16W60, 16R20

2. CMB 2014 (vol 57 pp. 609)

Nasr-Isfahani, Alireza
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 type.

Keywords:skew polynomial rings, Jacobson radical, derivation
Categories:16S36, 16N20

3. CMB 1999 (vol 42 pp. 298)

Jespers, Eric; Okniński, Jan
Semigroup Algebras and Maximal Orders
We describe contracted semigroup algebras of Malcev nilpotent semigroups that are prime Noetherian maximal orders.

Categories:16S36, 16H05, 20M25

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