CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Publicationsjournals
Publications        
Search results

Search: All articles in the CMB digital archive with keyword polynomial identities

  Expand all        Collapse all Results 1 - 2 of 2

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 2011 (vol 55 pp. 271)

Di Vincenzo, M. Onofrio; Nardozza, Vincenzo
On the Existence of the Graded Exponent for Finite Dimensional $\mathbb{Z}_p$-graded Algebras
Let $F$ be an algebraically closed field of characteristic zero, and let $A$ be an associative unitary $F$-algebra graded by a group of prime order. We prove that if $A$ is finite dimensional then the graded exponent of $A$ exists and is an integer.

Keywords:exponent, polynomial identities, graded algebras
Categories:16R50, 16R10, 16W50

© Canadian Mathematical Society, 2016 : https://cms.math.ca/