Maximal simultaneously nilpotent sets of matrices over antinegative semirings
| Autor: | Polona Oblak, David Dolžan |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Numerical Analysis Pure mathematics Algebra and Number Theory Mathematics::Rings and Algebras 010103 numerical & computational mathematics 02 engineering and technology Unipotent Central series 01 natural sciences Nilpotent matrix Upper and lower bounds Set (abstract data type) Mathematics::Group Theory Nilpotent 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics 020201 artificial intelligence & image processing Geometry and Topology 0101 mathematics Nilpotent group Mathematics::Representation Theory Zero divisor Mathematics |
| Zdroj: | Linear Algebra and its Applications. 510:222-229 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2016.08.014 |
| Popis: | We study the simultaneously nilpotent index of a simultaneously nilpotent set of matrices over an antinegative commutative semiring S . We find an upper bound for this index and give some characterizations of the simultaneously nilpotent sets when this upper bound is met. In the special case of antinegative semirings with all zero divisors nilpotent, we also find a bound on the simultaneously nilpotent index for all nonmaximal simultaneously nilpotent sets of matrices and establish their cardinalities in case of a finite S . |
| Databáze: | OpenAIRE |
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