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On semigroups and semirings of nonnegative matrices. (English) Zbl 1256.15016

The reader can find two results that are based on a generalization of a result of S. K. Jain, E. K. Kwak, and V. K. Goel [Trans. Am. Math. Soc. 257, 371–385 (1980; Zbl 0459.15008)]. Any finite multiplicative semigroup generated by a nonnegative matrix and a semiring of nonnegative matrices is characterized.

MSC:

15B48 Positive matrices and their generalizations; cones of matrices
20M25 Semigroup rings, multiplicative semigroups of rings
15A09 Theory of matrix inversion and generalized inverses
15A30 Algebraic systems of matrices
16Y60 Semirings

Citations:

Zbl 0459.15008
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Full Text: DOI

References:

[1] Ben-Israel Adi, Generalized Inverses and Applications (2003) · Zbl 1026.15004
[2] Berman A, Nonnegative Matrices in Mathematical Sciences (1994)
[3] DOI: 10.2307/2689442 · Zbl 0321.15008
[4] Jain SK, Math. Stud. Indian Mathematical Society 46 pp 42– (1978)
[5] DOI: 10.1090/S0002-9947-1980-0552264-3
[6] DOI: 10.1080/03081087708817182 · Zbl 0371.05014
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