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This is a Quantitative Study study.

October 16, 2025Open Access

On the PI-exponent of matrix algebras and algebras with generalized actions

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The study computes the PI-exponent of matrix algebras, revealing unique traits tied to their dimensionality.
It demonstrates that if two matrix algebras satisfy the same polynomial identities, then their dimensions must be equal.
Counterexamples are provided to illustrate what happens when an algebra does not meet the PI condition.
The findings also apply to certain finite-dimensional algebras with generalized actions over algebraically closed fields.

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Analysis shows polynomial identities distinguish matrix algebras with positive PI-exponent, suggesting unique dimensions.

Mello et al. (2025) studied this question.

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