Lawless order

W. Charles Holland; Alan H. Mekler; Saharon Shelah

doi:10.1007/BF00582744

Lawless order

W. Charles Holland^*
, Alan H. Mekler
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	383-397
Number of pages	15
Journal	Order
Volume	1
Issue number	4
DOIs	https://doi.org/10.1007/BF00582744
State	Published - Dec 1985

Keywords

AMS (MOS) subject classifications (1980): Primary 06F15, 06A05, secondary 03E99
Ordered groups
varieties

Access to Document

10.1007/BF00582744

Cite this

@article{3efdc3bb2764465e8d611bc5a68b0ad7,

title = "Lawless order",

abstract = "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.",

keywords = "AMS (MOS) subject classifications (1980): Primary 06F15, 06A05, secondary 03E99, Ordered groups, varieties",

author = "Holland, \{W. Charles\} and Mekler, \{Alan H.\} and Saharon Shelah",

year = "1985",

month = dec,

doi = "10.1007/BF00582744",

language = "אנגלית",

volume = "1",

pages = "383--397",

journal = "Order",

issn = "0167-8094",

publisher = "Springer Netherlands",

number = "4",

}

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 - https://www.scopus.com/pages/publications/34250120159

U2 - 10.1007/BF00582744

DO - 10.1007/BF00582744

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:34250120159

SN - 0167-8094

VL - 1

SP - 383

EP - 397

JO - Order

JF - Order

IS - 4

ER -

Lawless order

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this