Research Information System
Thesis Type: Postgraduate
Institution Of The Thesis: Marmara University, Faculty of Arts and Sciences, Mathematics, Turkey
Approval Date: 2020
Thesis Language: Turkish
Student: BARAN DÜZGÜN
Supervisor: Ünsal Tekir
Abstract:
In this paper, we introduce the notion of S-semiprime ideal which is a generalization of semiprime ideal. Let R be a commutative ring with a nonzero identity and S⊆R a multiplicatively closed set. An ideal P of R with P∩S=∅ is said to be an S-semiprime ideal if there exists s∈S and whenever x^m∈P for some m∈N and x∈R, then sx∈P. By using the definition of S-semiprime we investigate the relations between S-semiprime ideal and prime, semiprime, maximal ideal. Searching that in which situation these definitions are equal and giving examples and inverse examples about it. At last by using S-semiprime ideals we characterize reduced rings. In particular, R is said to be an S-reduced ring if there exists s∈S and whenever x^m=0 for some m∈N and x∈R, then sx=0.