A Note on Algebras that are Sums of Two Subalgebras

Canadian mathematical bulletin

Marek Kȩpczyk¹ 

[1] Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15--351 Białystok, Poland

关键词: rings with polynomial identities;    prime rings;   

DOI  :  10.4153/CMB-2015-082-6

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We study an associative algebra $A$ over an arbitrary field,that isa 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 wegeneralize this result for semiprime algebras $A$.Consider the class ofall 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 polynomialidentity.

【 授权许可】

Unknown