The semigroup of Hall matrices over distributive lattices
type: Item
instance of: scholarly article
title: The semigroup of Hall matrices over distributive lattices
zbMATH Open document ID: 0970.20047
DOI: 10.1007/PL00006027
published in: Semigroup Forum
publication date: 2001-10-22T00:00:00Z
review text: Let \(L\) be a complete and completely distributive lattice with the least and greatest elements \(0\) and \(1\), and let \(M_n(L)\) be the set of all \(n\times n\) matrices over \(L\). Clearly, \(M_n(L)\) is a semigroup with respect to a naturally defined product of matrices (where the meet stands for multiplication and join for addition). Matrices that are greater (under the naturally defined order) than invertible matrices are called Hall matrices, and form a subsemigroup \(H_n(L)\) of \(M_n(L)\). The author describes Green's relations in \(H_n(L)\), considers regular elements of \(H_n(L)\) and also looks at certain derived semigroups of \(H_n(L)\).
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 06D10
zbMATH DE Number: 1523496
zbMATH Keywords: completely distributive lattices
zbMATH Keywords: products of matrices
zbMATH Keywords: invertible matrices
zbMATH Keywords: Hall matrices
zbMATH Keywords: Green's relations
zbMATH Keywords: regular elements
zbMATH Keywords: derived semigroups
author: Yijia Tan
reviewed by: Boris M. Schein
MaRDI profile type: Publication
full work available at URL: pl00006027
OpenAlex ID: W2087301987
description: scientific article; zbMATH DE number 1523496