On the structure of S-2-prime ideals in noncommutative rings

This paper investigates right S-2-prime ideals in noncommutative rings, extending the concept of 2-prime and right S-prime ideals and their related structures. A proper ideal Y ⊆ H such that Y ∩ S = ∅ where S is an m-system, is called S-2-prime if for all elements x, y ∈ H satisfying xHy ⊆ Y, there is s ∈ S such that either x2〈s〉 ⊆ Y or y2〈s〉 ⊆ Y. We present various characterizations of these ideals, particularly in domains and prime rings. One of the key results includes a characterization for prime rings, along with conditions under which right S-2-prime ideals exhibit specific properties, such as the IFP property in certain domains. This study broadens the framework of 2-prime and S-prime ideals and provides deeper insights into their structure across different ring settings.