Abstract Let f: A→ B and g: A→ C be two ring homomorphisms and let J and J′ be ideals of
B and C, respectively, such that f− 1 (J)= g− 1 (J′). In this paper, we investigate the transfer …

This paper investigates necessary and sufficient conditions for a bi-amalgamation to inherit
the clean as well as the nil-clean properties. The new results recovers different settings of …

Let A be the fiber product R× TB, where B→ T is a surjective ring homomorphism with
regular kernel and R⊆ T is a ring extension where T is an overring of R. In this paper we …

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 …

This thesis is divided in two chapters. The first one concerns direct-sum decompositions in
additive categories. It is well known that if a module admits a direct-sum decomposition into …