Abstract
Let \(\mathfrak {R}\) be a ring graded by an arbitrary set A. We show that \(\mathfrak {R}\) decomposes as the sum of the well-described graded ideals plus (maybe) a certain subgroup. We also provide a context where the graded simplicity of \(\mathfrak {R}\) is characterized and where a second Wedderburn-type theorem in the category of arbitrarily graded rings is stated.
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Acknowledgements
The authors would like to thank the referee for his review of the paper as well as for his suggestions which have helped to improve the work. This work was supported by the PCI of the UCA ‘Teoría de Lie y Teoría de Espacios de Banach’, the PAI with project numbers FQM298 and FQM7156, and by the project of the Spanish Ministerio de Educación y Ciencia MTM2016-76327C31P.
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Izquierdo, F.J.N., Martín, A.J.C. On arbitrarily graded rings. Proc Math Sci 129, 20 (2019). https://doi.org/10.1007/s12044-018-0458-4
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DOI: https://doi.org/10.1007/s12044-018-0458-4