On Near Armendariz Ideals: Khadijeh Khalilnezhad, Hamid Haj Seyyed Javadi - Team, Support (Thai Journal of Mathematics, 2015)
We say a left ideal I is a near Armendariz whenever polynomials‎ ‎(x) f = f_0‎ + ‎f_1 x‎ + ‎…‎ + ‎f_m x^m‎, ‎(x) g = g_0‎ + ‎g_1 x‎ + ‎…‎ + ‎g_n x^n R [x] satisfy (x) f o (x)g r_R[x](I[x]) then g_j f_ir_R(I) for each 1≤ i ≤ m‎, ‎1≤ j ≤ n and (f_0)gr_R(I)‎. ‎The behavior of the left near Armendariz ideal condition isinvestigated with respect to various constructions‎. ‎It is shown that every left ideal of a near Armendariz ring is a near Armendariz left ideal‎. ‎Examples are included to illustrate and delimit the theory‎.