Multiplication of matrices over lattices
Rings and Algebras
2020-01-15 v1
Abstract
We study the multiplication operation of square matrices over lattices. If the underlying lattice is distributive, then matrices form a semigroup; we investigate idempotent and nilpotent elements and the maximal subgroups of this matrix semigroup. We prove that matrix multiplication over nondistributive lattices is antiassociative, and we determine the invertible matrices in the case when the least or the greatest element of the lattice is irreducible.
Cite
@article{arxiv.2001.04656,
title = {Multiplication of matrices over lattices},
author = {Kamilla Kátai-Urbán and Tamás Waldhauser},
journal= {arXiv preprint arXiv:2001.04656},
year = {2020}
}
Comments
17 pages, 3 figures