  In this paper, we introduce the notion of almost Armendariz ring which is the
generalization of Armendariz ring and discuss some of its properties. We prove
that a ring R is almost Armendariz if and only if n X n upper triangular matrix
ring T_{n}(R) is almost Armendariz ring. Similarly, If R is almost Armendariz
if and only if R[x] is almost Armendariz. It is observed that every almost
Armendariz ring is weak Armendariz but converse need not be true. But, if R is
semicommutative ring, then weak Armendariz ring is almost Armendariz ring.
Moreover, the class of minimal noncommutative almost Armendariz rings is
completely determined, up to isomorphism (minimal means having smallest
cardinality).
