On the representation of lattices by subsemigroup lattices of bands
type: Item
instance of: scholarly article
title: On the representation of lattices by subsemigroup lattices of bands
zbMATH Open document ID: 0852.20048
DOI: 10.1007/BF02573645
published in: Semigroup Forum
publication date: 1996-12-08T00:00:00Z
full work available at URL: https://eudml.org/doc/135424
review text: The main results of the paper are Theorems 1 and 2. Theorem 1 gives a description of (finite) lattices which are embeddable in subsemigroup lattices of (finite) rectangular bands. Theorem 2 describes simple finite lattices which are embeddable in subsemigroup lattices of finite bands. As a corollary of Theorem 2 the author proves that the partition lattice of a set with \(\geq 3\) elements cannot be embeddable in the subsemigroup lattice of a finite band.
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 06B15
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 815968
zbMATH Keywords: lattices embeddable in subsemigroup lattices
zbMATH Keywords: simple finite lattices
zbMATH Keywords: subsemigroup lattices of finite bands
zbMATH Keywords: partition lattices
author: Vladimir B. Repnitskiǐ
reviewed by: Boris Vernikov
MaRDI profile type: Publication
cites work: Two embedding theorems for lower bounded lattices
cites work: Q3848243
cites work: Q4165426
cites work: On finite lattices which are embeddable in subsemigroup lattices
cites work: On the representation of lattices by subgroup lattices
cites work: Q4001717
description: scientific article; zbMATH DE number 815968