Definition: $R$ is called Armendariz if whenever $(\sum a_ix^i)(\sum b_jx^j)=0\in R[x]$, then $a_ib_j=0$ for all combinations of $i,j$.

- D. D. Anderson and V. Camillo. Armendariz rings and Gaussian rings. (1998) @ .
- M. B. Rege, S. Chhawchharia, and others. Armendariz rings. (1997) @ .

- passes to subrings
- stable under finite products
- stable under products
- passes to polynomial rings