… characterize when a direct sum of hollow modules over a right perfect ring is direct
projective H-supplemented… First we consider when a direct sum of hollow modules is H-supplemented…

… supplemented modules and δ-supplemented modules. We characterize I-semiregular, I-semiperfect
and I-perfect rings … Note that I-semiregular rings are left-right symmetric and R is (δ−) …

… is a δ-perfect ring then every left R-module has the property (δ… A module M is called
supplemented if every submodule of M … We give an analogous characterization of our modules …

… characterization of the relations between amply supplemented and some concepts as,
semi-perfect, perfect … It is clear that R is a right perfect ring and hence R is an amply supplemented …

… We also prove that a ring R is a right (semi-)perfect ring if and only if (cyclic) lifting right R-module
has a … Next we characterize rings R such that every cyclic right R-module is lifting. …

… details of supplemented modules and left perfect rings, we refer … In particular, we give a
characterization of left perfect rings. … Right ss-perfect rings are defined similarly. R is said to be ss-…

… supplemented modules are also investigated. We present new characterizations of Z2(RR)-semiperfect
rings and SI-rings … this kind of modules, we prove that R is right SI-ring if and only …

… strongly local modules and rings. We show that every left strongly local ring is left perfect and
right perfect. … In this section we obtain new characterizations of semiperfect rings via their ss-…

… A large number of rings have characterizations in terms of … short exact sequence of right (or
left) R-modules splits if and … called as supplemented modules and supplementing modules, …

… Perfect and semiperfect rings were generalized to 𝛿-perfect … In Section 4, we study the
notion of 𝛿-semiperfect and 𝛿-perfect semirings. We also characterize subtractive 𝛿-semiperfect …