  In this paper, the notion of central Armendariz rings relative to a monoid is
introduced which is a generalization of central Armendariz rings and
investigate their properties. It is shown that if R is central reduced, then R
is M-central Armendariz for a u.p.-monoid M. For a monoid M and ring R, we
prove if R is an M-central Armendariz, then either R is commutative or M is
cancellative. Various examples which illustrate and delimit the results of this
paper are provided.
