Syarat perlu ring dan modul deret pangkat Noetherian

SOFNIDAR, Dr. Sri Wahyuni, MS

2003 | Tesis | S2 Matematika

Misalkan S monoid terurut tegas, R ring komutatif dengan elemen satuan, M modul atas R maka A = {f ÃŽ RS | supp(f) Artinian dan Narrow}adalah ring deret pangkat dan E = {j ÃŽ MS | supp(j) Artinian dan Narrow} adalah modul deret pangkat yang merupakan generalisasi dari ring dan modul deret pangkat formal R[[X]] dan M[[X]]. Dalam tesis ini dibahas syarat perlu ring dan modul deret pangkat Noetherian.

Let S be a strictly ordered monoid, R a commutative ring with an identity element, M a module over R, than the ring of generalized power series A is defined as A = {f ÃŽ RS | supp(f) Artinian dan Narrow}and the module of generalized power series E is defined as E = {j ÃŽ MS | supp(j) Artinian dan Narrow}. It is a generalized of the formalized power series ring R[[X]] and module M[[X]]. In this thesis it is studied the necessary conditions for Noetherian generalized power series rings and modules.

Kata Kunci : Matematika,Ring dan Model Noetherian, Ordered monoid, cancellative monoid, Noetherian rings and modules