In this paper, we introduce the notion of Ratliff-Rush closure of modules and
explore whether the condition of the Ratliff-Rush closure coincides with the
integral closure. The main result characterizes the condition in terms of the
normality of the projective scheme of the Rees algebra, which generalizes the
result of S. Goto and N. Matsuoka. In conclusion, we shall give a criterion for
the Buchsbaum Rees algebras.Comment: 15 page
