The Category G - GrR - Mod and Group Factorization

Rahmah Al-Omari and Mohammed Al-Shomrani ()
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Rahmah Al-Omari: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Mohammed Al-Shomrani: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2024, vol. 12, issue 21, 1-14

Abstract: In this work, we use the concept of G -weak graded rings and G -weak graded modules, which are based on grading by a set G of left coset representatives for the left action of a subgroup H of a finite X on X , to define the conjugation action of the set G and to generalize and prove some results from the literature. In particular, we prove that a G -weak graded ring R is strongly graded if and only if each G -weak graded R -module V is induced by an R e G -module. Moreover, we prove that the additive induction functor ( − ) R and the restriction functor ( − ) e G form an equivalence between the categories G - GrR - Mod and R e G - Mod when R is strongly G -weak graded. Furthermore, some related results and illustrative examples of G -weak graded R-modules and their morphisms are provided.

Keywords: left coset representatives; weak graded rings; weak graded module; weak graded homomorphisms; equivalence between categories (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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