Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on Green’s relations on the semigroup $N_{n}.$


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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 ${N_n},n \geqslant 3,\mathcal {D} \ne \mathcal {J}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20M10

Retrieve articles in all journals with MSC: 20M10


Additional Information

Keywords: Green’s relations, matrix equations, nonnegative matrices, regularity
Article copyright: © Copyright 1976 American Mathematical Society