IDEALIZATION OF QUASI MULTIPLICATION SUBMODULE ON LOCAL MODULE

• Main Author: Wijaya, Angga
• Format: Theses
• Language: Indonesia
• Subjects: Matematika
• Online Access: https://digilib.itb.ac.id/gdl/view/34756
• Institution: Institut Teknologi Bandung

Let ???? is a module over ring ????. Module ???? is called multiplication module if every submodule of ???? is formed by ????????. Next there is theory about prime submodule that generalize multiplication module to weak multiplication module. Module ???? is called weak multiplication module if every prime submodule of ???? is formed by [????: ????]????, with [????: ????] is the residual ideal. Then there is defined a set ????(????) and support of a module. This is used in module that almost multiplication or called quasi multiplication module. Module ???? is called quasi multiplication module if ????(????) = ???????? for every ???? in support of module ????. In conclusion, every multiplication module is quasi multiplication module, and every quasi multiplication module is weak multiplication module. Meanwhile, there is method of simplification submodule problem to ideal that is called idealization of a module. This is obtained by constructing a set ????(+)???? with some addition and multiplication operations to be a ring, with 0(+)???? is an ideal of ring ????(+)????. There is also simplification theory that makes into local problems that is localization theory. By localization theory in a prime ideal ???? of ????, it can be constructed a local module ???????? and local ring ????????. In this thesis, will be proven that a module ???? over ring ???? is quasi multiplication module if and only if the localization module ???????? is also quasi multiplication module over local ring ???????? for every ???? prime ideal in ????. Moreover, idealization of quasi multiplication submodule on local module is a quasi multiplication ideal.