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- Title
Serre condition for category of gradual modules.
- Authors
Salamian, Saeed; Jara, Pascual
- Abstract
In this paper, we first describe the gradual modules and the homomorphisms between two gradual modules. Next, we introduce the category G-Mod, whose objects are all gradual modules and morphisms are all homomorphisms between two gradual modules. Also, according to the definition of the gradual module's structure induced on each homomorphism f , we consider the gradual module's structure on ker f and Coker f. We show that being a monomorphism (respectively, epimorphism) in the category G-Mod is equivalent to a monomorphism (respectively, epimorphism) in the category R -Mod. As the main result, we prove that in any short exact sequence 0 → M ′ → M → M ″ → 0 , in R -Mod, if the R -module M has a gradual module's structure, then there are gradual module's structure on the modules M ′ and M ″ where the short exact sequence created is a short exact sequence in the category G-Mod.
- Subjects
HOMOMORPHISMS; MORPHISMS (Mathematics); DEFINITIONS
- Publication
Journal of Algebra & Its Applications, 2023, Vol 22, Issue 10, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498823502249