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Orthogonality graphs of matrices over commutative rings

Published 5 Aug 2022 in math.AG and math.RA | (2208.03039v2)

Abstract: The paper is devoted to studying the orthogonality graph of the matrix ring over a commutative ring. It is proved that the orthogonality graph of the ring of matrices with size greater than 1 over a commutative ring with zero-divisors is connected and has diameter 3 or 4; a criterion for each value is obtained. It is also shown that each of its vertices has distance at most 2 from some scalar matrix.

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Authors (1)

  1. O. G. Styrt 

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