Paper Info
Title
Hnn Extensions Of Semilattices
Abstract
The main purpose of this paper is to investigate properties of an HNN extension of a semilattice, to give its equivalent characterizations and to discuss similarities with free groups. An HNN extension of a semilattice is shown to be a universal object in a certain category and an F-inverse cover over a free group for every inverse semigroup in the category. We also show that a graph with respect to a certain subset of an HNN extension of a semilattice is a tree and that this property characterizes an HNN extension of a semilattice. Moreover, we look into three subclasses: the class of full HNN extensions of semilattices with an identity, the class of universally E-unitary inverse semigroups and the class of HNN extensions of finite semilattices. The first class consists of factorizable E-unitary inverse semigroups whose maximal group homomorphic images are free. We obtain a generalization of the Nielsen-Schreier subgroup theorem to this class. The second consists of inverse semigroups presented by relations on Dyck words. An inverse semigroup in the third class has a relatively easy finite presentation using a Dyck language and has solvable word problem.
Year
DOI
Venue
1999
10.1142/S0218196799000345
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
Field
DocType
Volume
Inverse,Discrete mathematics,Combinatorics,Algebra,Inverse semigroup,Word problem (mathematics education),Bass–Serre theory,Semilattice,Dyck language,HNN extension,Mathematics,Free group
Journal
9
Issue
ISSN
Citations 
5
0218-1967
2
PageRank 
References 
Authors
0.63
5
1
Name
Order
Citations
PageRank
Akihiro Yamamura19613.29