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On Graded Second and Coprimary Modules and Graded Secondary Representations

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Abstract

In this paper we introduce and study the concepts of graded second (gr-second) and graded coprimary (gr-coprimary) modules which are different from second and coprimary modules over arbitrary-graded rings. We list some properties and characterizations of gr-second and gr-coprimary modules and also study graded prime submodules of modules with gr-coprimary decompositions. We also deal with graded secondary representations for graded injective modules over commutative-graded rings. By using the concept of \(\sigma \)-suspension \((\sigma )M\) of a graded module \(M,\) we prove that a graded injective module over a commutative graded Noetherian ring has a graded secondary representation.

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Acknowledgments

The first author thanks the Scientific Technological Research Council of Turkey (TUBITAK) for the financial support. The authors were supported by the Scientific Research Project Administration of Akdeniz University.

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Authors and Affiliations

  1. Department of Mathematics, Akdeniz University, Antalya, Turkey

    Seçil Çeken & Mustafa Alkan

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  1. Seçil Çeken
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  2. Mustafa Alkan
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Correspondence to Seçil Çeken.

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Communicated by Siamak Yassemi.

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Çeken, S., Alkan, M. On Graded Second and Coprimary Modules and Graded Secondary Representations. Bull. Malays. Math. Sci. Soc. 38, 1317–1330 (2015). https://doi.org/10.1007/s40840-014-0097-6

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  • DOI: https://doi.org/10.1007/s40840-014-0097-6

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