DIRECTED SUBMODULES IN PARTIALLY ORDERED MODULES

• Main Author: Noviani, Enik
• Format: Theses
• Language: Indonesia
• Subjects: Matematika
• Online Access: https://digilib.itb.ac.id/gdl/view/33690
• Institution: Institut Teknologi Bandung

A module over a totally ordered ring equiped with ordered relation that is compatible to its binary operations is called a partially ordered modules. There are several classes of partially ordered modules such as directed partially ordered modules ang lattice modules. In the literature there are number of characterization of an ideal in a latttice vector spaces such as sublattice and full subspace, solid subspace, sublattice and the kernel of a positive linier mapping, as well as the kernel of the homomorphism lattice. This thesis study those characterization and generalize to lattice modules over totally ordered lattice ring. It will also be shown that characterzation of directed full subspace in a lattice vector space can be generalizes to directed submodules.