Publication: Zayıf asal idealler
Abstract
Zayıf Asal İdealler Bu tezin ana amacı birimli ve değişmeli halkalarda zayıf asal idealleri ve zayıf asalımsı idealleri çalışmaktır. Bu amaçla ilk olarak zayıf asal ideal kavramı tanımlanmış, temel özellikleri ve farklı karakterizasyonları incelenmiştir. Daha sonra zayıf asal ideallere benzer şekilde zayıf asalımsı ideal kavramı tanımlanmış ve zayıf asal idealler için elde edilen bulguların zayıf asalımsı idealler için de gerçeklenip gerçeklenmediği araştırılmıştır. Ayrıca halkalara benzer olarak modüller için de asal ve zayıf asal alt modül kavramları tanımlanıp bunların temel özellikleri incelenmiştir. Son olarak değişmeli halkalar üzerinde çarpımsal modül kavramı tanımlanmış ve özel olarak bu modüllerin asal ve zayıf asal alt modülleri ile ilgili sonuçlar elde edilmiştir. Anahtar Kelimer: Zayıf Asal İdeal, Zayıf Asal Alt Modül, Zayıf Asalımsı İdeal, Zayıf Asalımsı Alt Modül
Weakly Prime Ideals 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. Key words: Weakly Prime İdeal, Weakly Prime Submodule, Weakly Primary İdeal, Weakly Primary Submodule
Weakly Prime Ideals 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. Key words: Weakly Prime İdeal, Weakly Prime Submodule, Weakly Primary İdeal, Weakly Primary Submodule