CHARACTERIZATION A FINITELY GENERATED DEDEKIND MODULES OVER ORDER MODULE

• Main Author: Ode Sirad, La
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/34873
• Institution: Institut Teknologi Bandung

Let R be a commutative ring with unity and T be the multiplicative set of all regular elements in R. A fraction ring of R, can be constructed such that R can be embedded into RT (-1). One of the relation between a ring and a module is given by an order of the module 0(M). The order of the module is known as a commutative ring. Moreover, it is a subring of a fraction ring. A ring whose every non-zero ideal is invertible called a Dedekind ring. The concept of an invertible ideal in a ring will be generated into a module theory. In a module theory, its already developed the concept of an invertible submodule. Therefore, a Dedekind module can be defined. Studying relation between M as an R-module and as a 0(M)-module gives that the properties of M as a 0(M)-module can be identified from M as an R-module. A 0(M)-module will be known as a Dedekind module, the order of M will be a Dedekind ring and it is an integrally closed if M is a finitely generated Dedekind R-module. The main result is studying about characteristics of a finitely generated Dedekind module related to the properties of the order of modules.