Invertible and nilpotent matrices over antirings

DOI10.1016/j.laa.2008.07.016zbMath1155.15019arXiv0806.2996OpenAlexW2962728383MaRDI QIDQ958019

Polona Oblak, David Dolžan

Publication date: 2 December 2008

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.2996

zbMATH Keywords

nilpotent matrixinvertible matrixantiring

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Semirings (16Y60)

Related Items

Invertible matrices over a class of semirings ⋮ Minimal orderings and quadratic forms on a free module over a supertropical semiring ⋮ Decompositions of modules lacking zero sums ⋮ On simultaneously nilpotent antiring matrices ⋮ Inner products on semimodules over a commutative semiring. ⋮ Invertible matrices and semilinear spaces over commutative semirings ⋮ The unitary Cayley graph of a semiring ⋮ Bases in semimodules over commutative semirings ⋮ Invertible matrices over finite additively idempotent semirings ⋮ Cholesky decomposition of matrices over commutative semirings ⋮ Supertropical SL_n ⋮ Noncommuting graphs of matrices over semirings ⋮ Commuting graphs of matrices over semirings. ⋮ Bijective linear rank preservers for spaces of matrices over antinegative semirings ⋮ On nilpotent subsemigroups of the matrix semigroup over an antiring. ⋮ On nilpotency of matrices over antirings ⋮ Unnamed Item ⋮ Idempotent matrices over antirings ⋮ Algebras with a negation map

Cites Work

• Unnamed Item
• On invertible matrices over antirings
• On nilpotent matrices over antirings
• On the number of labeled acyclic digraphs
• Arc colorings of digraphs
• Sums and products of quasi-nilpotent operators
• Sums of square-zero operators

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