Graded Rings Associated with Factorizable Finite Groups

Mohammed M. Al-Shomrani () and Najla Al-Subaie
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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

Mathematics, 2023, vol. 11, issue 18, 1-14

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.

Keywords: weak graded rings; weak graded modules; factorizable finite groups; left coset representatives (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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