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Orthogonality Graphs of Direct Sums of Rings and Semisimple Artinian Rings

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The paper studies the orthogonality relation graphs for noncommutative rings. Known results on the diameters of the connected components of simple Artinian rings are generalized to larger ring classes, particularly, to semisimple Artinian and semiprime two-sided Goldie rings. Also the presence of isolated vertices in the graphs of the above ring classes is considered, and the behavior of the diameter function under taking a direct sum for pairs of arbitrary rings is studied.

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Authors and Affiliations

  1. Lomonosov Moscow State University; Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia

    O. V. Markova

  2. Lomonosov Moscow State University, Moscow, Russia

    D. Yu. Novochadov

Authors
  1. O. V. Markova
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  2. D. Yu. Novochadov
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Correspondence to O. V. Markova.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 514, 2022, pp. 138–166.

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Markova, O.V., Novochadov, D.Y. Orthogonality Graphs of Direct Sums of Rings and Semisimple Artinian Rings. J Math Sci 272, 574–591 (2023). https://doi.org/10.1007/s10958-023-06451-9

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  • DOI: https://doi.org/10.1007/s10958-023-06451-9

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