On generalization of primeness in module category
Issued Date
2023
Copyright Date
2015
Language
eng
File Type
application/pdf
No. of Pages/File Size
v, 61 leaves
Access Rights
restricted access
Rights Holder(s)
Mahidol University
Bibliographic Citation
Thesis (Ph.D. (Mathematics))--Mahidol University, 2015
Suggested Citation
Nguyen, Dang Hoa Nghiem, 1984- On generalization of primeness in module category. Thesis (Ph.D. (Mathematics))--Mahidol University, 2015. Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/89751
Title
On generalization of primeness in module category
Author(s)
Abstract
Prime ideals play an important role in the study of ring structures, especially in commutative algebras. Motivating the definition of prime submodules of Sanh et al. in 2008, we introduced and investigated the class of IFP and nearly prime submodules. Using our notions, we generalized the Anderson's Theorem, following that for a finitely generated, quasi-projective, fully IFP module M, which is a self-generator, if every minimal prime submodule over a proper fully invariant submodule U of M is finitely generated, then there are finitely many minimal prime submodules over U. The main result in this thesis is that a finitely generated right R-module is Noetherian if and only if every nearly prime submodule is finitely generated. This can be considered as a generalization of Cohen's Theorem in commutative rings.
Degree Name
Doctor of Philosophy
Degree Level
Doctoral Degree
Degree Department
Faculty of Science
Degree Discipline
Mathematics
Degree Grantor(s)
Mahidol University