Communications of the
Korean Mathematical Society CKMS

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 $a^{n}Rcap b^{n}R$ 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 non-finite conductor weakly finite conductor rings.

Keywords: Almost weakly finite conductor rings, weakly finite conductor rings, trivial rings extension, amalgamated algebra along an ideal

MSC numbers: 15A03, 13A15, 13B25, 13D05, 13F05