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Keywords:
half linearly ordered group; lexicographic product; isomorphic refinements
half linearly ordered group; lexicographic product; isomorphic refinements
Summary:
The notion of the half linearly ordered group (and, more generally, of the half lattice ordered group) was introduced by Giraudet and Lucas [2]. 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. The analogous problem for linearly ordered groups was dealt with by Maltsev [5]; his result was generalized by Fuchs [1] and the author [3]. The isomorphic refinements of small direct product decompositions of half lattice ordered groups were studied in [4].
References:
[1] L. Fuchs: Partially Ordered Algebraic Systems. Pergamon Press, Oxford-London-New York-Paris, 1963. MR 0171864 | Zbl 0137.02001
[2] M. Giraudet and F. Lucas: Groupes à moitié ordonnés. Fund. Math. 139 (1991), 75–89. DOI 10.4064/fm-139-2-75-89 | MR 1150592
[3] J. Jakubík: The mixed product decompositions of partially ordered groups. Czechoslovak Math. J. 20 (1970), 184–206. MR 0258705
[4] J. Jakubík: On half lattice ordered groups. Czechoslovak Math. J. 46 (1996), 745–767. MR 1414606
[5] A. I. Maltsev: On ordered groups. Izv. Akad. Nauk SSSR, ser. matem., 38 (1951), 473–482. (Russian) MR 0032645
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