Bi-amalgamations subject to j-clean and weakly j-clean properties

Abstract

This paper establishes the necessary and sufficient conditions for a bi-amalgamation to inherit the J-clean and weakly J-clean properties in the commutative setting. The new results recover previous works carried on these rings in amalgamations and trivial extensions, also, they are used to provide new examples and counterexamples of J-clean and weakly J-clean rings arise as bi-amalgamations.