A right R-module N is called pseudo M-injective if for any submodule A of M, every monomorphism f... more A right R-module N is called pseudo M-injective if for any submodule A of M, every monomorphism from A to N, can be extended to a homomorphism from M to N. Module M is called pseudo injective if M is pseudo M-injective. Some characterizations of classes modules and its applications to classical rings are studied. In this paper, we consider some generalizations pseudo injective modules under monomorphism of their closed submodules. Their properties are studied.
Following (Kosan in Algebra Colloq. 14:53-60, 2007), a module M is called δsupplemented if, for e... more Following (Kosan in Algebra Colloq. 14:53-60, 2007), a module M is called δsupplemented if, for every submodule of N of M, there exists L ≤ N such that M = N + L and N ∩L δ L. A module M is called δ-lifting if, for any N ≤ M, there exists a decomposition M = A ⊕ B such that A ≤ N and N ∩ B δ M. In this paper, we study e-supplemented modules and e-lifting modules which are generalized δ-supplemented modules and δ-lifting modules. Some properties of these modules are considered. Moreover, we also have new characterizations of Artinian (resp., Noetherian) Rad e (M) module studied with chain conditions on e-supplemented modules.
A right R-module N is called pseudo M-injective if for any submodule A of M, every monomorphism f... more A right R-module N is called pseudo M-injective if for any submodule A of M, every monomorphism from A to N, can be extended to a homomorphism from M to N. Module M is called pseudo injective if M is pseudo M-injective. Some characterizations of classes modules and its applications to classical rings are studied. In this paper, we consider some generalizations pseudo injective modules under monomorphism of their closed submodules. Their properties are studied.
Following (Kosan in Algebra Colloq. 14:53-60, 2007), a module M is called δsupplemented if, for e... more Following (Kosan in Algebra Colloq. 14:53-60, 2007), a module M is called δsupplemented if, for every submodule of N of M, there exists L ≤ N such that M = N + L and N ∩L δ L. A module M is called δ-lifting if, for any N ≤ M, there exists a decomposition M = A ⊕ B such that A ≤ N and N ∩ B δ M. In this paper, we study e-supplemented modules and e-lifting modules which are generalized δ-supplemented modules and δ-lifting modules. Some properties of these modules are considered. Moreover, we also have new characterizations of Artinian (resp., Noetherian) Rad e (M) module studied with chain conditions on e-supplemented modules.
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