# 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: 46
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)