Paper Info
Title
Bounded Homomorphisms And Finitely Generated Fiber Products Of Lattices
Abstract
We investigate when fiber products of lattices are finitely generated and obtain a new characterization of bounded lattice homomorphisms onto lattices satisfying a property we call Dean's condition (D) which arises from Dean's solution to the word problem for finitely presented lattices. In particular, all finitely presented lattices and those satisfying Whitman's condition satisfy (D). For lattice epimorphisms g : A -> D, h: B -> D, where A, B are finitely generated and D satisfies (D), we show the following: If g and h are hounded, then their fiber product (pullback) C = {(a,b) is an element of A x B vertical bar g(a) = h(b)} is finitely generated. While the converse is not true in general, it does hold when A and B are free. As a consequence, we obtain an (exponential time) algorithm to decide boundedness for finitely presented lattices and their finitely generated sublattices satisfying (D). This generalizes an unpublished result of Freese and Nation.
Year
DOI
Venue
2020
10.1142/S0218196720500174
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
Keywords
DocType
Volume
Free lattice, finitely presented lattice, Whitman's condition, bounded lattice, subdirect product, pullback
Journal
30
Issue
ISSN
Citations 
4
0218-1967
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
William DeMeo100.34
Peter Mayr253.34
Nik Ruskuc313.11