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Graded Prime Submodules over Non-Commutative Rings

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Abstract

Let G be a group, R be an associative ring and M be a G-graded R-module. In this article, we study graded prime submodules over non-commutative rings; we call them graded total prime submodules; several results concerning such submodules are given. The advantage that graded total prime modules have over graded prime ones is highlighted and different situations that lead to graded total prime modules are given.

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Acknowledgements

The authors express their very special thanks to the referees whose comments have helped to improve the exposition of this article.

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Authors and Affiliations

  1. Department of Mathematics, Yarmouk University, Irbid, Jordan

    Rashid Abu-Dawwas & Maaly Al-Muanger

  2. Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan

    Malik Bataineh

Authors
  1. Rashid Abu-Dawwas
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  2. Malik Bataineh
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  3. Maaly Al-Muanger
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Correspondence to Malik Bataineh.

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Abu-Dawwas, R., Bataineh, M. & Al-Muanger, M. Graded Prime Submodules over Non-Commutative Rings. Vietnam J. Math. 46, 681–692 (2018). https://doi.org/10.1007/s10013-018-0274-2

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  • DOI: https://doi.org/10.1007/s10013-018-0274-2

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