ALMOST WEAKLY FINITE CONDUCTOR RINGS AND WEAKLY FINITE CONDUCTOR RINGS

Let R be a commutative ring with identity. We call the ring R to be an almost weakly finite conductor if for any two elements a and b in R, there exists a positive integer n such that anR ∩ bnR is finitely generated. In this article, we give some conditions for the trivial ring extensions and the amalgamated algebras to be almost weakly finite conductor rings. We investigate the transfer of these properties to trivial ring extensions and amalgamation of rings. Our results generate examples which enrich the current literature with new families of examples of nonfinite conductor weakly finite conductor rings.