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Search: MSC category 16W60 ( Valuations, completions, formal power series and related constructions [See also 13Jxx] )

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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

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