«lattice ordered group»
۲۷۲۱ نتیجهA classification of hull operators in archimedean lattice-ordered groups with unit
The category, or class of algebras, in the title is denoted by $bf W$. A hull operator (ho) in $bf W$ is a reflection in the category consisting of $bf W$ objects with only essential embeddings as morphisms. The proper class of all of these is $bf hoW$. The bounded monocoreflecti
Existentially Complete Abelian Lattice-ordered Groups
The theory of abelian totally ordered groups has a model completion. We show that the theory of abelian lattice-ordered groups has no model companion. Indeed, the Archimedean property can be captured by a first order V3V sentence for existentially complete abelian lattice-ordered
Archimedean - like Classes of Lattice - Ordered Groups
Suppose <? denotes a class of totally ordered groups closed under taking subgroups and quotients by o-homomorphisms. We study the following classes: (1) Res (£?), the class of all lattice-ordered groups which are subdirect products of groups in C; (2) Hyp(C), the class of lattice
Locally Solid Topological Lattice-ordered Groups
Locally solid Riesz spaces have been widely investigated in the past several decades; but locally solid topological lattice-ordered groups seem to be largely unexplored. The paper is an attempt to initiate a relatively systematic study of locally solid topological lattice-ordered
Finitely generated lattice-ordered groups with soluble word problem
William W. Boone and Graham Higman proved that a finitely generated group has soluble word problem if and only if it can be embedded in a simple group that can be embedded in a finitely presented group. We prove the exact analogue for lattice-ordered groups: Theorem: A finitely g
on fuzzy convex lattice-ordered subgroups
in this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. also, the fuzzy convex subgroup (resp. fuzzy con
Proof theory for lattice-ordered groups
Proof theory can provide useful tools for tackling problems in algebra. In particular, Gentzen systems admitting cut-elimination have been used to establish decidability, complexity, amalgamation, admissibility, and generation results for varieties of residuated lattices correspo
A Class of Simple Lattice-ordered Groups
A lattice-ordered group (/-group) is said to be regular il no positive element of the group is disjoint from any of its conjugates. It is well known that every simple regular /-group is totally ordered [S]. The subgroups of the reals are the most elementary examples of regular si
On fuzzy convex lattice-ordered subgroups
In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy con
Sets of Disjoint Elements in Free Products of Lattice-ordered Groups
We show that for every infinite cardinal number m there exist two totally ordered abelian groups whose free product in any nontrivial variety of lattice-ordered groups has a disjoint set of cardinality m. This answers problem 10.7 of [13] and extends the results in [12]. We furth