Distinguished completion of a direct product of lattice ordered groups
Czechoslovak Mathematical Journal (2001)
- Volume: 51, Issue: 3, page 661-671
- ISSN: 0011-4642
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topJakubík, Ján. "Distinguished completion of a direct product of lattice ordered groups." Czechoslovak Mathematical Journal 51.3 (2001): 661-671. <http://eudml.org/doc/30662>.
@article{Jakubík2001,
abstract = {The distinguished completion $E(G)$ of a lattice ordered group $G$ was investigated by Ball [1], [2], [3]. An analogous notion for $MV$-algebras was dealt with by the author [7]. In the present paper we prove that if a lattice ordered group $G$ is a direct product of lattice ordered groups $G_i$$(i\in I)$, then $E(G)$ is a direct product of the lattice ordered groups $E(G_i)$. From this we obtain a generalization of a result of Ball [3].},
author = {Jakubík, Ján},
journal = {Czechoslovak Mathematical Journal},
keywords = {lattice ordered group; distinguished completion; direct product; lattice ordered group; distinguished completion; direct product},
language = {eng},
number = {3},
pages = {661-671},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Distinguished completion of a direct product of lattice ordered groups},
url = {http://eudml.org/doc/30662},
volume = {51},
year = {2001},
}
TY - JOUR
AU - Jakubík, Ján
TI - Distinguished completion of a direct product of lattice ordered groups
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 3
SP - 661
EP - 671
AB - The distinguished completion $E(G)$ of a lattice ordered group $G$ was investigated by Ball [1], [2], [3]. An analogous notion for $MV$-algebras was dealt with by the author [7]. In the present paper we prove that if a lattice ordered group $G$ is a direct product of lattice ordered groups $G_i$$(i\in I)$, then $E(G)$ is a direct product of the lattice ordered groups $E(G_i)$. From this we obtain a generalization of a result of Ball [3].
LA - eng
KW - lattice ordered group; distinguished completion; direct product; lattice ordered group; distinguished completion; direct product
UR - http://eudml.org/doc/30662
ER -
References
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- 10.1007/BF01190971, Algebra Univ. 35 (1996), 85–112. (1996) Zbl0842.06012MR1360533DOI10.1007/BF01190971
- Lattice Ordered Groups, Tulane University, 1970. (1970) Zbl0258.06011
- Generalized Dedekind completion of a lattice ordered group, Czechoslovak Math. J. 28 (1978), 294–311. (1978) MR0552650
- Maximal Dedekind completion of an abelian lattice ordered group, Czechoslovak Math. J. 28 (1978), 611–631. (1978) MR0506435
- 10.1023/A:1022469521480, Czechoslovak Math. J. 49 (1999), 867–876. (1999) MR1746712DOI10.1023/A:1022469521480
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