A BRIANÇN-SKODA THEOREM AND THE COHEN-MACAULAYNESS OF REES MODULES
Results on the Cohen-Macaulayness of a Rees ring and the associated graded ring are generalised to a Rees module R(I, N) and the associated graded module G(I, N) for N finitely generated module and I an ideal of definition of N. The tight closure of an ideal with respect to a module is defined and a relationship between the integral closure and the tight closure with respect to N is obtained.
Cohen-Macaulay, Rees modules, graded module, Brian篮-Skoda Theorem.
