Property: Armendariz

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 $i,j$.

Resources for learning about this property:

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

Metaproperties:

This property has the following metaproperties
  • passes to subrings
  • stable under finite products
  • stable under products
  • passes to polynomial rings