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A note on Green's relations on the semigroup $ N\sb{n}.$


Authors: D. J. Hartfiel, C. J. Maxson and R. J. Plemmons
Journal: Proc. Amer. Math. Soc. 60 (1976), 11-15
MSC: Primary 20M10
DOI: https://doi.org/10.1090/S0002-9939-1976-0419655-7
MathSciNet review: 0419655
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Abstract: Solvability criteria for nonnegative matrix equations are applied in characterizing the first three of the four Green's relations $ \mathcal{L},\mathcal{R},\mathcal{D}$ and $ \mathcal{J}$ on the semigroup $ {N_n}$ of all $ n \times n$ nonnegative matrices. For the relation $ \mathcal{J}$, it is shown that $ \mathcal{D} = \mathcal{J}$ when the relation is restricted to the regular matrices in $ {N_n}$ although on the entire semigroup $ {N_n},n \geqslant 3,\mathcal{D} \ne \mathcal{J}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0419655-7
Keywords: Green's relations, matrix equations, nonnegative matrices, regularity
Article copyright: © Copyright 1976 American Mathematical Society

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