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|Examples of this include the study of ideals and divisibility, dating back to the work of Dedekind and continued by Krull; the pioneering work of Hahn on totally ordered abelian groups; and the work of Kantorovich and other analysts on ...|
|;This work is intended for pure and applied mathematicians and algebraists interested in topics such as group, order, number and lattice theory, universal algebra, and representation theory; and upper-level undergraduate and graduate ...|
|A complemented modular lattice L is said to be irreducible if any two atomic |
elements have a common complement. G. Lattice-Ordered Groups An ordered
set G in which a group operation is defined is called an ordered group when x jú
|Theorem B If G is a lattice-ordered group that can be embedded ex- plicitly in a |
finitely presented lattice-ordered group and H is any o-group that can be
embedded explicitly in an o-group that is finitely presented as a lattice-ordered
group and ...
|In this chapter we present the most basic parts of the theory of lattice-ordered |
groups. Though our main concern will eventually be with abelian groups it is not
appreciably harder to develop this material within the class of all groups.
|A. M. W. GLASS Using ultraproducts, N. R. Reilly proved that if G is a |
representable lattice-ordered group and J is an independent subset totally
ordered by <, then the order on G can be extended to a total order which induces
< on J (see ).
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