S-semiprime ideals of commutative rings

Thesis Type: Postgraduate

Institution Of The Thesis: Marmara University, Faculty of Arts and Sciences, Mathematics, Turkey

Approval Date: 2020

Thesis Language: Turkish


Supervisor: Ünsal Tekir


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.