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- Title
On generalized injective modules and almost injective modules.
- Authors
Fuchigami, Hayate; Kuratomi, Yosuke; Shibata, Yoshiharu
- Abstract
A module M is called N -almost-invariant for a module N if, for any homomorphism α : F → E , either α (N) ⊆ M , or there exist nonzero direct summands F ′ of F and E ′ of E such that α | F ′ : F ′ → E ′ is an isomorphism and (α | F ′ ) − 1 (M ∩ E ′) ⊆ N ∩ F ′ , where E and F are the injective hulls of M and N , respectively. This is a generalization of an almost N -injective module. In this paper, we give a new characterization of a generalized N -injective module by homomorphisms between their injective hulls, and consider conditions for an N -almost-invariant module to be almost N -injective. Moreover, we study a relationship between generalized N -injective, almost N -injective and N -almost-invariant modules.
- Subjects
ISOMORPHISM (Mathematics); NOETHERIAN rings
- Publication
Journal of Algebra & Its Applications, 2024, Vol 23, Issue 2, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498824500270