Research Information System
Thesis Type: Postgraduate
Institution Of The Thesis: Marmara University, Institute for Graduate Studies in Pure and Applied Sciences, Department of Mathematics, Turkey
Approval Date: 2010
Thesis Language: Turkish
Student: TAYLAN TOZOĞLU
Supervisor: Ünsal Tekir
Abstract:
The main purpose of this thesis is to study the weakly prime ideals and the weakly primary ideals of the commutative rings with identity.For this purpose, firstly the notion of weakly prime ideal has been defined, the fundamental properties and different characterizations of them have been investigated. Thereafter, analogously to the weakly prime ideals, the notion of weakly primary ideal has been given and it has been investigated whether the same findings we obtained for weakly prime ideals are true for weakly primary ideals. In addition to these, as in the case of rings, we have defined for modules the notion of prime and weakly prime submodule and investigated their fundamental properties.Finally, the notion of multiplication module over commutative ring has been given and particularly the results about prime and weakly prime submodules of these modules have been obtained