The study of groups equipped with a compatible lattice order ("lattice-ordered groups" or "I!-groups") has arisen in a number of different contexts. 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 partially ordered function spaces. After the Second World War, the theory of lattice-ordered groups became a subject of study in its own right, following the publication of fundamental papers by Birkhoff, Nakano and Lorenzen. The theory blossomed under the leadership of Paul Conrad, whose important papers in the 1960s provided the tools for describing the structure for many classes of I!-groups in terms of their convex I!-subgroups. A particularly significant success of this approach was the generalization of Hahn's embedding theorem to the case of abelian lattice-ordered groups, work done with his students John Harvey and Charles Holland. The results of this period are summarized in Conrad's "blue notes" [C].

We need your support!
Make a donation to help us stay online
        
Bitcoin (BTC)
bc1q08g9d22cxkawsjlf8etuek2pc9n2a3hs4cdrld
	
Bitcoin Cash (BCH)
qqvwexzhvgauxq2apgc4j0ewvcak6hh6lsnzmvtkem

Ethereum (ETH)
0xb55513D2c91A6e3c497621644ec99e206CDaf239

Litecoin (LTC)
ltc1qt6g2trfv9tjs4qj68sqc4uf0ukvc9jpnsyt59u

USDT (ERC20)
0xb55513D2c91A6e3c497621644ec99e206CDaf239

USDT (TRC20)
TYdPNrz7v1P9riWBWZ317oBgJueheGjATm