A NOTE ON QUASI-ARMENDARIZ RINGS

A ring R is called a quasi-Armendariz ring if whenever elements α = a₀+a₁x+a₂x²+· · ·+a_nxⁿ, β = b₀+b₁x+b₂x²+· · ·+b_mx^m ∈ R[x] satisfy αR[x]β = 0, then a_iRb_j = 0 for each i, j. In this note we consider quasi-Armendariz property of a special subring of the infinite upper triangular matrix ring over a ring R.