Matrices over semirings
type: Item
instance of: scholarly article
title: Matrices over semirings
zbMATH Open document ID: 0884.15010
DOI: 10.1016/0020-0255(95)00283-9
author: Shamik Ghosh
published in: Information Sciences
publication date: 1998-03-10T00:00:00Z
review text: Let \(R\) be a commutative semiring with multiplicative identity \(1 \neq 0\) (for example, the nonnegative integers), and let \(M_{n}(R)\) denote the semiring of \(n \times n\) matrices over \(R\). Because the condition of invertibility in \(M_{n}(R)\) is rather restrictive in this situation, the author introduces the concept of ``semi-invertibility'': \(A \in M_{n}(R)\) is semi-invertible if there exist \(A_{1}, A_{2} \in M_{n}(R)\) such that \(I+ AA_{1} = AA_{2}\) and \(I+ A_{1}A = A_{2}A\). Some more or less straightforward generalizations of criteria for invertibility when \(R\) is a ring are made to give criteria for semi-invertibility in the semiring case.
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 16Y60
zbMATH DE Number: 1071950
zbMATH Keywords: matrices over semirings
zbMATH Keywords: semi-invertibiltiy
reviewed by: John D. Dixon
MaRDI profile type: Publication
full work available at URL: 0020-0255(95)00283-9
OpenAlex ID: W1998549077
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cites work: Linear operators strongly preserving idempotent matrices over semirings
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cites work: Q4023553
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description: scientific article; zbMATH DE number 1071950