STRONGLY J-N-COHERENT RINGS

. Let R be a ring and n a fixed positive integer. A right R-module M is called strongly J-n-injective if every R-homomorphism from an n-generated small submodule of a free right R-module F to M extends to a homomorphism of F to M; a right R-module V is said to be strongly J-n-flat, if for every ngenerated small submodule T of a free left R-module F, the canonical map V 0 T -> V 0 F is monic; a ring R is called left strongly J-n-coherent if every n-generated small submodule of a free left R-module is finitely presented; a ring R is said to be left J-n-semihereditary if every n-generated small left ideal of R is projective. We study strongly J-n-injective modules, strongly J-n-flat modules and left strongly J-n-coherent rings. Using the concepts of strongly J-n-injectivity and strongly J-n-flatness of modules, we also present some characterizations of strongly J-n-coherent rings and J-n-semihereditary rings.