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Graded Rings Associated with Factorizable Finite Groups

Author

Listed:
  • Mohammed M. Al-Shomrani

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Najla Al-Subaie

    (Department of Mathematics, Taif University, Taif 26571, Saudi Arabia)

Abstract

Let R be an associative ring with unity, X be a finite group, H be a subgroup of X , and G be a set of left coset representatives for the left action of H on X . In this article, we introduce two different ways to put R into a non-trivial G -weak graded ring that is a ring graded by the set G which is defined with a binary operation ∗ and satisfying an algebraic structure with specific properties. The first one is by choosing a subset S of G such that S is a group under the ∗ operation and putting R t = 0 for all t ∈ G and t ∉ S . The second way, which is the most important, is induced by combining the operation ∗ defined on G and the coaction ◁ of H on G . Many examples are provided.

Suggested Citation

  • Mohammed M. Al-Shomrani & Najla Al-Subaie, 2023. "Graded Rings Associated with Factorizable Finite Groups," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3864-:d:1236730
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    References listed on IDEAS

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    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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