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Subdirect decompositions and the radical of a generalized Boolean algebra extension of a lattice ordered group
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 733-754
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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 $R(A_B)$.
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 $R(A_B)$.
Classification : 06F15, 06F20
Keywords: lattice ordered group; generalized Boolean algebra; extension; vector lattice; subdirect decomposition; value; radical 
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     title = {Subdirect decompositions and the radical of a generalized {Boolean} algebra extension of a lattice ordered group},
     journal = {Czechoslovak Mathematical Journal},
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}
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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, Tome 56 (2006) no. 2, pp. 733-754. http://geodesic.mathdoc.fr/item/CMJ_2006_56_2_a35/

[1] G. Birkhoff: Lattice Theory. Third Edition, Providence, 1967. | MR | Zbl

[2] P. Conrad: Lattice Ordered Groups. Tulane University, 1970. | Zbl

[3] P. Conrad and M. R. Darnel: Generalized Boolean algebras in lattice ordered groups. Order 14 (1998), 295–319. | MR

[4] P. Conrad and M. R. Darnel: Subgroups and hulls of Specker lattice-ordered groups. Czechoslovak Math. J 51 (2001), 395–413. | DOI | MR

[5] C. Goffman: Remarks on lattice ordered groups and vector lattices. I. Carathéodory functions. Trans. Amer. Math. Soc. 88 (1958), 107–120. | MR | Zbl

[6] J. Jakubík: Cardinal properties of lattice ordered groups. Fundamenta Math. 74 (1972), 85–98. | DOI | MR

[7] J. Jakubík: Torsion classes of Specker lattice ordered groups. Czechoslovak Math. J. 52 (2002), 469–482. | DOI | MR

[8] J. Jakubík: On vector lattices of elementary Carathéodory functions. Czechoslovak Math. J 55 (2005), 223-236. | DOI | MR

[9] J. Jakubík: Torsion classes and subdirect products of Carathéodory vector lattices. Math. Slovaca 56 (2006), 79–92. | MR

[10] J. Jakubík: Generalized Boolean algebra extensions of lattice ordered groups. Tatra Mt. Math. Publ. 30 (2005), 1–19. | MR

[11] F. Šik: Über subdirekte Summen geordneter Gruppen. Czechoslovak Math. J. 10 (1960), 400–424. | MR