In this work, we prove that an R-module M is cofinitely δ-supplemented (ie each cofinite
submodule of M has a δ-supplement) if and only if every maximal submodule of M has a δ-
supplement. An R-module M is called cofinitely δ-semiperfect if each finitely generated factor
module of M has a projective δ-cover, we prove that this is equivalent to the existence of a δ-
supplement, which is a direct summand of M, for each cofinite submodule of M. Cofinitely δ-
lifting modules are introduced and characterized. We also give new characterizations of δ …

… By a module M is called cofinitely (amply resp.) δ-supplemented if every cofinite module
in M has a (an ample resp.) δ-supplement M is called ⊕cofinitely δ-supplemented if every
cofinite submodel of M has a δ-supplement which is a direct summand of M. If every factor …
By the semiperfect in σ[M] and cofinitely δ-semiperfect we introduce the notation cofintely
δM -semiperfect modules and study their basic properties. We also characterize these
modules using the notation cofinitely δM -supplemented modules . …