Perfect Semiring of Nonnegative Matrices

Adel Alahmedi (), Yousef Alkhamees () and S. K. Jain ()
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Adel Alahmedi: King Abdulaziz University, Department of Mathematics
Yousef Alkhamees: Kinf Saud University, Department of Mathematics
S. K. Jain: King Abdulaziz University, Department of Mathematics

A chapter in Combinatorial Matrix Theory and Generalized Inverses of Matrices, 2013, pp 177-181 from Springer

Abstract: Abstract In this paper, it is shown that the semiring of nonnegative matrices satisfies descending chain condition on right and left ideals, i.e., it is left or right perfect if and only if it is closed under Drazin inverse of all elements. Furthermore, each nonnil right and left ideal contains a nonzero idempotent. This generalizes the known result on the characterization of finite semigroups of nonnegative matrices.

Keywords: Perfect semiring; Artinian semiring; Nonnegative matrices; Drazin inverse; 15A09; 16Y60 (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-1053-5_15

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DOI: 10.1007/978-81-322-1053-5_15

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