  Even if a ring A is coherent, the polynomial ring A[X] in one variable could
fail to be coherent. In this note we show that A[X] is graded coherent with the
standard grading deg X=1. More generally, we give a criterion of graded
coherentness of the tensor algebra T_{A}(M) of a certain class of bi-module M.
  As an application of the criterion, we show that there is a relationship
between higher dimensional Auslander-Reiten theory and graded coherentness of
higher preprojective algebras.
