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The Category G - GrR - Mod and Group Factorization

Author

Listed:
  • 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)

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.

Suggested Citation

  • Rahmah Al-Omari & Mohammed Al-Shomrani, 2024. "The Category G - GrR - Mod and Group Factorization," Mathematics, MDPI, vol. 12(21), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3344-:d:1506458
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    References listed on IDEAS

    as
    1. M. M. Al-Shomrani & E. J. Beggs, 2004. "Making nontrivially associated modular categories from finite groups," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-34, January.
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