Let R be a commutative ring with unity. A closure operation on the set of ideals of a commutative ring R (respectively the set of fractional ideals of R or the R-submodules of Q) is a function : I(R) ! I(R) (respectively : F(R) ! F(R) or c : F(R) ! F(R)) satisfying one) (Extention) I I c for all I 2 I(R) (I 2 F(R) or I 2 F(R)). two) (Order Preservation) If I J then I c J c. three) (Idempotence) (I c)c = I c for all I 2 I(R) (I 2 F(R) or I 2 F(R)). A clousure operation c on the set of ideals to be star if for all regular elements u 2 R and all I 2 I(R), (uI)c = uI c. And also a closure operation c : I(R) ! I(R) is standard if ((xI)c : x) = I c for any regular element x 2 R. In this thesis, we study semistar operation on the ring R = k[[x; y]]=(xy) for a feld k. In particular we show that R has 24 semistar operations
عنوان اصلی به زبان دیگر
عنوان اصلي به زبان ديگر
Star, semistar and standard operations
نام شخص به منزله سر شناسه - (مسئولیت معنوی درجه اول )