Subdirect decompositions and the radical of a generalized Boolean algebra extension of a lattice ordered group

Ján Jakubík

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 2, page 733-754
  • ISSN: 0011-4642

Abstract

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The extension of a lattice ordered group by a generalized Boolean algebra will be denoted by . In this paper we apply subdirect decompositions of for dealing with a question proposed by Conrad and Darnel. Further, in the case when is linearly ordered we investigate (i) the completely subdirect decompositions of and those of , and (ii) the values of elements of and the radical .

How to cite

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Jakubík, Ján. "Subdirect decompositions and the radical of a generalized Boolean algebra extension of a lattice ordered group." Czechoslovak Mathematical Journal 56.2 (2006): 733-754. <http://eudml.org/doc/31063>.

@article{Jakubík2006,
abstract = {The extension of a lattice ordered group $A$ by a generalized Boolean algebra $B$ will be denoted by $A_B$. In this paper we apply subdirect decompositions of $A_B$ for dealing with a question proposed by Conrad and Darnel. Further, in the case when $A$ is linearly ordered we investigate (i) the completely subdirect decompositions of $A_B$ and those of $B$, and (ii) the values of elements of $A_B$ and the radical $R(A_B)$.},
author = {Jakubík, Ján},
journal = {Czechoslovak Mathematical Journal},
keywords = {lattice ordered group; generalized Boolean algebra; extension; vector lattice; subdirect decomposition; value; radical; lattice-ordered group; generalized Boolean algebra},
language = {eng},
number = {2},
pages = {733-754},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Subdirect decompositions and the radical of a generalized Boolean algebra extension of a lattice ordered group},
url = {http://eudml.org/doc/31063},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Jakubík, Ján
TI - Subdirect decompositions and the radical of a generalized Boolean algebra extension of a lattice ordered group
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 2
SP - 733
EP - 754
AB - The extension of a lattice ordered group $A$ by a generalized Boolean algebra $B$ will be denoted by $A_B$. In this paper we apply subdirect decompositions of $A_B$ for dealing with a question proposed by Conrad and Darnel. Further, in the case when $A$ is linearly ordered we investigate (i) the completely subdirect decompositions of $A_B$ and those of $B$, and (ii) the values of elements of $A_B$ and the radical $R(A_B)$.
LA - eng
KW - lattice ordered group; generalized Boolean algebra; extension; vector lattice; subdirect decomposition; value; radical; lattice-ordered group; generalized Boolean algebra
UR - http://eudml.org/doc/31063
ER -

References

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