New Results About Some Chain Conditions in Serre Conjecture Rings

Abstract

Let φ:T→T/I be the natural homomorphism, where I is a nonzero ideal of an integral domain T. We define R:=φ−1(D), where D is a subring of T/I. This paper aims to investigate the conditions under which the Serre conjecture ring R⟨m⟩ is a strong S-domain. Several examples are constructed to demonstrate both the scope and limitations of the results.