Geodesic
Lexicographic products of half linearly ordered groups
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 1, pp. 127-138
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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].
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].
Classification : 06F15
Keywords: half linearly ordered group; lexicographic product; isomorphic refinements 
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Jakubík, Ján. Lexicographic products of half linearly ordered groups. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 1, pp. 127-138. http://geodesic.mathdoc.fr/item/CMJ_2001_51_1_a11/

[1] L.  Fuchs: Partially Ordered Algebraic Systems. Pergamon Press, Oxford-London-New York-Paris, 1963. | MR | Zbl

[2] M.  Giraudet and F.  Lucas: Groupes à moitié ordonnés. Fund. Math. 139 (1991), 75–89. | DOI | MR

[3] J.  Jakubík: The mixed product decompositions of partially ordered groups. Czechoslovak Math.  J. 20 (1970), 184–206. | MR

[4] J.  Jakubík: On half lattice ordered groups. Czechoslovak Math.  J. 46 (1996), 745–767. | MR

[5] A. I.  Maltsev: On ordered groups. Izv. Akad. Nauk SSSR, ser. matem., 38 (1951), 473–482. (Russian) | MR