When every finitely generated regular ideal is principal

Abstract In this paper, we introduce a ring in which every finitely generated regular ideal is principal, and we call it a regular Bézout ring. We investigate the stability of this property under localization and homomorphic image, and its transfer to various contexts of constructions such as trivial ring extensions, pullbacks and amalgamated duplication of a ring along an ideal. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.