On nilpotency of matrices over antirings
type: Item
instance of: scholarly article
title: On nilpotency of matrices over antirings
zbMATH Open document ID: 1202.15021
author: Yijia Tan
published in: Linear Algebra and its Applications
publication date: 2010-10-22T00:00:00Z
review text: An antiring is a semiring which is zerosumfree (i.e., \(a+b=0\) implies \(a=b=0\) for any \(a,b\) in this semiring). The author studies the nilpotency of matrices over commutative antirings. He provides some properties and characterizations of the nilpotent matrices in terms of principal permanental minors, main diagonals and permanental adjoint matrices. When a family of matrices are simultaneously considered, he establishes some characterizations of the simultaneous nilpotency for a family of matrices.
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 16Y60
zbMATH DE Number: 5804411
zbMATH Keywords: semiring
zbMATH Keywords: antiring
zbMATH Keywords: nilpotent matrix
zbMATH Keywords: simultaneous nilpotency
zbMATH Keywords: permanent
zbMATH Keywords: principal permanental minors
zbMATH Keywords: adjoint matrices
reviewed by: Andreas Arvanitoyeorgos
MaRDI profile type: Publication
full work available at URL: j.laa.2010.06.003
OpenAlex ID: W2084637837
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DOI: 10.1016/J.LAA.2010.06.003
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description: scientific article; zbMATH DE number 5804411