Two embedding theorems for lower bounded lattices
type: Item
instance of: scholarly article
title: Two embedding theorems for lower bounded lattices
zbMATH Open document ID: 0901.06005
DOI: 10.1007/BF01233912
author: Kira Adaricheva
published in: Algebra Universalis
publication date: 1998-11-24T00:00:00Z
review text: A finite lattice \(L\) is lower bounded if, for every homomorphism from a finitely generated free lattice into \(L,\) the preimage of an element of \(L\) has a smallest element whenever it is non-empty. Main results: Theorem 1. Every finite lower bounded lattice \(L\) can be embedded in a finite atomistic lower bounded lattice \(L_1\) with \(\big | J(L_1)\big | =\big | J(L)\big | .\) Theorem 2. A finite lattice \(L\) is lower bounded iff \(L\) can be embedded in the lattice \(\text{Sub}(P)\) of all subsemilattices of some finite semilattice \(P.\)
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 06B05
Mathematics Subject Classification ID: 06B25
Mathematics Subject Classification ID: 06A12
zbMATH DE Number: 1226556
zbMATH Keywords: finite lattice
zbMATH Keywords: lower bounded lattice
zbMATH Keywords: lattice of subsemilattices
MaRDI profile type: Publication
cites work: Characterizations of Finite Lattices that are Bounded-Homomqrphic Images or Sublattices of Free Lattices
cites work: Equational Bases and Nonmodular Lattice Varieties
cites work: On finite lattices which are embeddable in subsemigroup lattices
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description: scientific article; zbMATH DE number 1226556