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arXiv · 2008.11041

Representability of Noetherian PI-algebras

Be'eri Greenfeld·Louis Rowen
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Abstract

This note concerns the still open question of representability of Noetherian PI-algebras. Extending a result of Rowen and Small (with an observation of Bergman) that every finitely generated module over a commutative Noetherian ring containing a field is representable, we provide a representability machinery for a Noetherian PI-algebra $R$ containing a field, which includes the case that $R$ is finite (as a module) over a commutative subalgebra isomorphic to $R/N$. We construct a family of non-representable PI-algebras demonstrating the sharpness of these results, as well as of some well known previous representability results.

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Be'eri Greenfeld, Louis Rowen. 2020-08-25. Representability of Noetherian PI-algebras. https://arxiv.org/abs/2008.11041

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