Research Information System
Thesis Type: Doctorate
Institution Of The Thesis: Marmara University, Institute for Graduate Studies in Pure and Applied Sciences, Department of Mathematics, Turkey
Approval Date: 2016
Thesis Language: Turkish
Student: ECE YETKİN ÇELİKEL
Supervisor: Ünsal Tekir
Abstract:
In this study, the concepts of 2-absorbing primary and weakly 2-absorbing primary ideals are defined as a generalization of primary ideals in commutative rings. So generalizations of 2-absorbing and weakly 2-absorbing ideals which are defined in literature by A. Badawi as generalizations of prime and weakly prime ideals in commutative rings are obtained. The relations among the concepts of prime, weakly prime, primary, 2-absorbing primary ideal and 2-absorbing primary, weakly 2-absorbing primary ideals are investigated. Then we define 2-absorbing primary and weakly 2-absorbing primary submodules of multiplication modules over commutative rings and some basic properties are studied in detail. The lattice of ideals of a commutative ring with identity is a compactly generated principally generated modular lattice. However there are non-modular multiplicative lattices. The extensions of 2-absorbing and weakly 2-absorbing ideals of commutative rings to multiplicative lattices are obtained by defining 2-absorbing and weakly 2-absorbing elements. The relations among prime, weakly prime, primary and weakly primary elements in multiplicative lattices are investigated. Moreover some characterizations for some special lattices in terms of 2-absorbing and weakly 2-absorbing elements are obtained