# Property detail

Property name: polynomial identity

Definition: There exists an element of $\mathbb Z\langle x_1,\ldots x_n\rangle$ for which any set of $n$ ring elements satisfies the polynomials

Rings with property: 45

Rings without property: 0

## Metaproperties

This property has the following metaproperties

- passes to subrings
(theorem needed)
- passes to quotient rings
(theorem needed)
- stable under finite products
(theorem needed)