### On Near Armendariz Ideals

#### Abstract

We say a left ideal $I$ is a near Armendariz whenever polynomials

$(x) f = f_0 + f_1 x + \ldots + f_m x^m$, $(x) g = g_0 + g_1 x + \ldots + g_n x^n \in R [x]$ satisfy $(x) f o (x)g \in r_{R[x]}(I[x])$ then $ g_j f_i\in r_{R}(I)$ for each $1\leq i \leq m$, $1\leq j \leq n$ and $(f_0)g\in r_{R}(I)$.

The behavior of the left near Armendariz ideal condition is\linebreak investigated 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.

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