TY - JOUR
T1 - Lawless order
AU - Holland, W. Charles
AU - Mekler, Alan H.
AU - Shelah, Saharon
PY - 1985/12
Y1 - 1985/12
N2 - R. Baer asked whether the group operation of every (totally) ordered group can be redefined, keeping the same ordered set, so that the resulting structure is an Abelian ordered group. The answer is no. We construct an ordered set (G, ≤) which carries an ordered group (G, •, ≤) but which is lawless in the following sense. If (G, *, ≤) is an ordered group on the same carrier (G, ≤), then the group (G, *) satisfies no nontrivial equational law.
AB - R. Baer asked whether the group operation of every (totally) ordered group can be redefined, keeping the same ordered set, so that the resulting structure is an Abelian ordered group. The answer is no. We construct an ordered set (G, ≤) which carries an ordered group (G, •, ≤) but which is lawless in the following sense. If (G, *, ≤) is an ordered group on the same carrier (G, ≤), then the group (G, *) satisfies no nontrivial equational law.
KW - AMS (MOS) subject classifications (1980): Primary 06F15, 06A05, secondary 03E99
KW - Ordered groups
KW - varieties
UR - http://www.scopus.com/inward/record.url?scp=34250120159&partnerID=8YFLogxK
U2 - 10.1007/BF00582744
DO - 10.1007/BF00582744
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AN - SCOPUS:34250120159
SN - 0167-8094
VL - 1
SP - 383
EP - 397
JO - Order
JF - Order
IS - 4
ER -