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 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 ) .

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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  8. 10.1007/s10587-005-0017-x, Czechoslovak Math. J 55 (2005), 223-236. (2005) MR2121669DOI10.1007/s10587-005-0017-x
  9. Torsion classes and subdirect products of Carathéodory vector lattices, Math. Slovaca 56 (2006), 79–92. (2006) MR2217581
  10. Generalized Boolean algebra extensions of lattice ordered groups, Tatra Mt. Math. Publ. 30 (2005), 1–19. (2005) MR2190244
  11. Über subdirekte Summen geordneter Gruppen, Czechoslovak Math. J. 10 (1960), 400–424. (1960) MR0123626

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