ALMOST WEAKLY FINITE CONDUCTOR RINGS AND WEAKLY FINITE CONDUCTOR RINGS

Commun. Korean Math. Soc. Published online December 15, 2021

Hanan CHOULLI, Haitham EL ALAOUI, and Hakima MOUANIS
Faculty of Sciences Dhar Al Mahraz, Laboratory of geometric and arithmetic algebra, Fez, Morocco.; Faculty of Sciences Dhar Al Mahraz, Laboratory of geometric and arithmetic algebra, Fez, Morocco.; Faculty of Sciences Dhar Al Mahraz, Laboratory of geometric and arithmetic algebra, Fez, Morocco.

Abstract : Let R be a commutative ring with identity. We call the ring R
to be a 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 algebra to be almost weakly finite conductor rings. Also, we
give new characterizations of the property weakly finite conductor to trivial
ring extensions and amalgamated algebras along an ideal. In order to give
new results to 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.