Some Remarks on Fitting Ideals of Multiplication Modules

Some Remarks on Fitting Ideals of Multiplication Modules

Let R be a commutative ring and let M = M1 Ɵ M2 where M1;M2 be a finitely generated R-modules. We obtain the Fitting ideals of M. We prove the Fitting ideals of M are prin- cipal and cancelation if and only if AnnR(M1) and AnnR(M2) are principal and cancellation.