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On Modules over G-sets

Author

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  • Mehmet Uc

    (Burdur Mehmet Akif Ersoy University, Assistant Professor Doctor, Department of Mathematics, Burdur, Turkey)

  • Mustafa Alkan

    (Akdeniz University, Professor Doctor, Department of Mathematics, Burdur, Turkey)

Abstract

Let R be a commutative ring with unity, M a module over R and let S be a G–set for a finite group G. We define a set MS to be the set of elements expressed as the formal finite sum of the form ∑s∈Smss where ms∈M. The set MS is a module over the group ring RG under the addition and the scalar multiplication similar to the RG–module MG. With this notion, we not only generalize but also unify the theories of both of the group algebra and the group module, and we also establish some significant properties of (MS)RG. In particular, we describe a method for decomposing a given RG–module MS as a direct sum of RG–submodules. Furthermore, we prove the semisimplicity problem of (MS)RG with regard to the properties of MR, S and G.

Suggested Citation

  • Mehmet Uc & Mustafa Alkan, 2023. "On Modules over G-sets," Journal of Mathematics and Statistics Studies, Al-Kindi Center for Research and Development., vol. 4(4), pages 47-55, October.
    • Handle: RePEc:alk:jmss00:v:4:y:2023:i:4:id:6113
    DOI: 10.32996/jmss.2023.4.4.5
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