Lexicographic products of half linearly ordered groups
Czechoslovak Mathematical Journal (2001)
- Volume: 51, Issue: 1, page 127-138
- ISSN: 0011-4642
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topJakubík, 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
top- Partially Ordered Algebraic Systems, Pergamon Press, Oxford-London-New York-Paris, 1963. (1963) Zbl0137.02001MR0171864
- 10.4064/fm-139-2-75-89, Fund. Math. 139 (1991), 75–89. (1991) MR1150592DOI10.4064/fm-139-2-75-89
- The mixed product decompositions of partially ordered groups, Czechoslovak Math. J. 20 (1970), 184–206. (1970) MR0258705
- On half lattice ordered groups, Czechoslovak Math. J. 46 (1996), 745–767. (1996) MR1414606
- On ordered groups, Izv. Akad. Nauk SSSR, ser. matem., 38 (1951), 473–482. (Russian) (1951) MR0032645
Citations in EuDML Documents
top- Milan Demko, Lexicographic product decompositions of partially ordered quasigroups
- Milan Demko, Lexicographic product decompositions of half linearly ordered loops
- Ján Jakubík, Štefan Černák, On convex linearly ordered subgroups of an -group
- Štefan Černák, Cantor extension of a half lineary cyclically ordered group
- Ján Jakubík, On half cyclically ordered groups
- Ján Jakubík, On monotone permutations of -cyclically ordered sets
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