Lexicographic products of half linearly ordered groups

Ján Jakubík

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 1, page 127-138
  • ISSN: 0011-4642

Abstract

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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].

How to cite

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Jakubík, Ján. "Lexicographic products of half linearly ordered groups." Czechoslovak Mathematical Journal 51.1 (2001): 127-138. <http://eudml.org/doc/30620>.

@article{Jakubík2001,
abstract = {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].},
author = {Jakubík, Ján},
journal = {Czechoslovak Mathematical Journal},
keywords = {half linearly ordered group; lexicographic product; isomorphic refinements; half linearly ordered group; lexicographic product; isomorphic refinements},
language = {eng},
number = {1},
pages = {127-138},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Lexicographic products of half linearly ordered groups},
url = {http://eudml.org/doc/30620},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Jakubík, Ján
TI - Lexicographic products of half linearly ordered groups
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 1
SP - 127
EP - 138
AB - 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].
LA - eng
KW - half linearly ordered group; lexicographic product; isomorphic refinements; half linearly ordered group; lexicographic product; isomorphic refinements
UR - http://eudml.org/doc/30620
ER -

References

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  1. Partially Ordered Algebraic Systems, Pergamon Press, Oxford-London-New York-Paris, 1963. (1963) Zbl0137.02001MR0171864
  2. 10.4064/fm-139-2-75-89, Fund. Math. 139 (1991), 75–89. (1991) MR1150592DOI10.4064/fm-139-2-75-89
  3. The mixed product decompositions of partially ordered groups, Czechoslovak Math.  J. 20 (1970), 184–206. (1970) MR0258705
  4. On half lattice ordered groups, Czechoslovak Math.  J. 46 (1996), 745–767. (1996) MR1414606
  5. On ordered groups, Izv. Akad. Nauk SSSR, ser. matem., 38 (1951), 473–482. (Russian) (1951) MR0032645

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