#TITLE_ALTERNATIVE#

• Main Author: SUWASTIKA (NIM : 30110007), ERMA
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/20077
• Institution: Institut Teknologi Bandung

Structure of a ring is not always preserved on its polynomial ring. For examples,polynomial ring over Dedekind domain is not Dedekind domain and alsopolynomial ring over Dedekind prime ring is not Dedekind prime ring. To obtain aring whose structure is preserved on its polynomial ring, property of Dedekinddomain is weakened into a new structure named generalized Dedekind domain orG-Dedekind domain. Just like Dedekind domain, Dedekind prime ring can also begeneralized into a new structure named generalized prime ring or G-Dedekindprime ring. Structures of the obtained rings are preserved on their polynomial rings.Any polynomial ring over G-Dedekind domain remains G-Dedekind domain andany polynomial ring over G-Dedekind prime ring is also G-Dedekind prime ring.The definition of a Dedekind domain which is used in this dissertation is an integraldomain whose every nonzero ideal is invertible, while a G-Dedekind domain is anintegral domain whose every reflexive ideal is invertible. Meanwhile a Dedekindprime ring is a prime Goldie ring whose every nonzero ideal is invertible and a GDedekind prime ring is a prime Noetherian maximal order whose every reflexive ideal is invertible. A Dedekind prime ring is noncommutative Dedekind domain.This dissertation continues the previous researches to obtain the structures of ring which are preserved on their polynomial rings. This dissertation observes whether those structures are preserved on their skew polynomial rings. Discussion in this dissertation is divided into two areas, those are ring area andmodule area. On ring area we discuss the structure of polynomial rings and compare them to the structure of their base rings. The structures of rings which are discussed are the generalization of the rings that we have already known, such as G-Dedekind domain, G-Dedekind prime ring, and G-Asano prime ring. Besides discussion on ring area, this dissertation also contains discussion on module area. The module which is discussed in this area is Dedekind module. Adapting the generalization of Dedekind domain to G-Dedekind domain and Dedekind prime ring to G Dedekind prime ring, Dedekind module is also generalized to G- Dedekind module. Definition of G-Dedekind module is reserved in this dissertation. Relation between G-Dedekind domain and G-Dedekind module is also reserved. <br />