A study of w1-(w + n)-projective QTAG-modules

In this paper, we define a new class of w1 -(w + n)-projective module and study their basic properties. We proved that a module M is almost w1 -(w + n)- projective if and only if there exists a countably gen-erated nice submodule K which satisfies the inequalities Hw+n(M) # K # Hw(M) such that M=K is almost (w + n)-projective. (c) 2022 The Author(s). Published by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).