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arXiv · 1411.7395

Identities of sum of two PI-algebras in the case of positive characteristic

Ivan Kaygorodov·Artem Lopatin·Yury Popov
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Abstract

We consider the following question posted by K.I. Beidar and A.V. Mikhalev in 1995 for an associative ring $R=R_1+R_2$: is it true that if the subrings $R_1$ and $R_2$ satisfy polynomial identities, then $R$ also satisfies a polynomial identity? Over a field of positive characteristic we establish new conditions on $R_1$ and $R_2$ that guarantee a positive answer to the question. We find upper and low bounds on the degrees of identities of $R$.

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Ivan Kaygorodov, Artem Lopatin, Yury Popov. 2014-11-26. Identities of sum of two PI-algebras in the case of positive characteristic. https://doi.org/10.1142/s021819671550040x

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