Invertible and nilpotent matrices over antirings

Simple item page
dc.creatorDolžan, David
dc.creatorOblak, Polona
dc.date2008-06-18
dc.date2008-08-14
dc.date.accessioned2026-07-07T09:56:22Z
dc.date.available2026-07-07T09:56:22Z
dc.descriptionIn this paper we characterize invertible matrices over an arbitrary commutative antiring S and find the structure of GL_n (S). We find the number of nilpotent matrices over an entire commutative finite antiring. We prove that every nilpotent $n \times n$ matrix over an entire antiring can be written as a sum of $\lceil \log_2 n \rceil$ square-zero matrices and also find the necessary number of square-zero summands for an arbitrary trace-zero matrix to be expressible as their sum.
dc.description9 pages, 1 figure, minor changes
dc.identifierhttps://arxiv.org/abs/0806.2996
dc.identifierhttp://arxiv.org/abs/0806.2996
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/166952
dc.subjectCommutative Algebra
dc.subjectCombinatorics
dc.titleInvertible and nilpotent matrices over antirings
dc.typetext

Files

Collections

arXiv