# PI theory for Associative Pairs

## TL;DR

This paper extends classical associative PI-theory to Associative Pairs, introducing concepts like PI-elements, PI-ideals, extended centroid, and central closure within this new framework.

## Contribution

It develops a novel extension of associative PI-theory specifically tailored for Associative Pairs, including new notions analogous to those in algebra and Jordan systems.

## Key findings

- Introduction of PI-element and PI-ideal for Associative Pairs
- Development of extended centroid and central closure concepts
- Framework for further algebraic investigations in Associative Pairs

## Abstract

We extend the classical associative PI-theory to Associative Pairs, and in doing so, we introduce related notions already present for algebras (and Jordan systems) as the ones of PI-element and PI-ideal, extended centroid and central closure.

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Source: https://tomesphere.com/paper/1901.08833