zbMATH — the first resource for mathematics

Lexicographic products of half linearly ordered groups. (English) Zbl 1079.06504
Summary: The notion of the half linearly ordered group (and, more generally, of the half lattice ordered group) was introduced by M. Giraudet and F. Lucas [Fundam. Math. 139, 75-89 (1991; Zbl 0766.06014)].
In the present paper we define the lexicographic product of half linearly ordered groups. This definition includes as a particular case the lexicographic product of linearly ordered groups.
We investigate the problem of the existence of isomorphic refinements of two lexicographic product decompositions of a half linearly ordered group.

06F15 Ordered groups
Full Text: DOI EuDML
[1] L. Fuchs: Partially Ordered Algebraic Systems. Pergamon Press, Oxford-London-New York-Paris, 1963. · Zbl 0137.02001
[2] M. Giraudet and F. Lucas: Groupes à moitié ordonnés. Fund. Math. 139 (1991), 75-89. · Zbl 0766.06014
[3] J. Jakubík: The mixed product decompositions of partially ordered groups. Czechoslovak Math. J. 20 (1970), 184-206.
[4] J. Jakubík: On half lattice ordered groups. Czechoslovak Math. J. 46 (1996), 745-767. · Zbl 0879.06011
[5] A. I. Maltsev: On ordered groups. Izv. Akad. Nauk SSSR, ser. matem., 38 (1951), 473-482.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.