Free Lattice-Ordered Groups

1989 ◽  
pp. 206-227 ◽  
Author(s):  
Stephen H. McCleary
Keyword(s):  
Free Lattice ◽  
Ordered Groups ◽  
Lattice Ordered Groups

Representations of free lattice-ordered groups

Order ◽  
1993 ◽  
Vol 10 (4) ◽  
pp. 375-381 ◽  
Author(s):  
Manfred Droste
Keyword(s):  
Free Lattice ◽  
Ordered Groups ◽  
Lattice Ordered Groups

scholarly journals Free lattice-ordered groups

1970 ◽  
Vol 16 (2) ◽  
pp. 191-203 ◽  
Author(s):  
Paul Conrad
Keyword(s):  
Free Lattice ◽  
Ordered Groups ◽  
Lattice Ordered Groups

Free lattice-ordered groups

1979 ◽  
Vol 18 (4) ◽  
pp. 259-270 ◽  
Author(s):  
V. M. Kopytov
Keyword(s):  
Free Lattice ◽  
Ordered Groups ◽  
Lattice Ordered Groups

Countable lattice-ordered groups

1983 ◽  
Vol 94 (1) ◽  
pp. 29-33 ◽  
Author(s):  
A. M. W. Glass
Keyword(s):  
Free Lattice ◽  
Lattice Ordered Group ◽  
Ordered Group ◽  
Recursively Enumerable Set ◽  
Ordered Groups ◽  
Recursively Enumerable ◽  
Lattice Ordered Groups ◽  
Natural Analogues ◽  
Group Words ◽  
Combinatorial Group

A lattice-ordered group is a group and a lattice such that the group operation distributes through the lattice operations (i.e. f(g ∨ h)k = fgk ∨ fhk and dually). Lattice-ordered groups are torsion-free groups and distributive lattices. They further satisfy f ∧ g = (f−1 ∨ g−1)−1 and f ∨ g = (f−1 ∧ g−1)−1. Since the lattice is distributive, each lattice-ordered group word can be written in the form ∨A ∧B ωαβ where A and B are finite and each ωαβ is a group word in {xi: i ∈ I}. Unfortunately, even for free lattice-ordered groups, this form is not unique. We will use the prefix l- for maps between lattice-ordered groups that preserve both the group and lattice operations, and e for the identity element. A presentation (xi;rj(x) = e)i∈I, j∈J is the quotient of the free lattice-ordered group F on {xi: i∈I} by the l-ideal (convex normal sublattice subgroup) generated by its subset {rj(x): j ∈ J}. {xi: i ∈ I} is called a generating set and {ri(x):j∈J} a defining set of relations. If I and J are finite we have a finitely presented lattice-ordered group. If we can effectively enumerate all lattice-ordered group words r1(x), r2(x),… in xi; i∈I}. If I is finite and J (for this enumeration) is a recursively enumerable set, we say that we have a recursively presented lattice-ordered group. Throughout Z denotes the group of integers and ℝ the real line.Our purpose in this paper is to prove the natural analogues of three theorems from combinatorial group theory (5), chapter IV, theorems 4·9, 3·1 and 3·5-in particular, theorem C is a natural analogue of an unpublished theorem of Philip Hall (4).

scholarly journals Sequential convergences on free lattice ordered groups

1992 ◽  
Vol 117 (1) ◽  
pp. 48-54
Author(s):  
Ján Jakubík
Keyword(s):  
Free Lattice ◽  
Ordered Groups ◽  
Lattice Ordered Groups

Right-ordered and free lattice-ordered groups

1995 ◽  
Vol 34 (1) ◽  
pp. 18-22
Author(s):  
S. V. Varaksin
Keyword(s):  
Free Lattice ◽  
Ordered Groups ◽  
Lattice Ordered Groups
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