Geodesic
Vector Lattices on a~Set of Two Generators
Algebra i logika, Tome 41 (2002) no. 4, pp. 391-410.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that the center of an automorphism group $\operatorname{Aut}(FVL2)$ of a free vector lattice $FVL2$ on a set of two free generators is isomorphic to a multiplicative group of positive reals. It is shown that the free vector lattice $FVL2$ has an isomorphic representation by continuous piecewise linear functions of the real line; as a consequence, the ideal lattice and the root system for rectifying ideals in $FVL2$ are amply described. Similar results are obtained for a free vector lattice $FVL_Q2$ generated by two elements over a field of rational numbers.
Keywords: free vector lattice, center of an automorphism group, ideal lattice, root system. 
@article{AL_2002_41_4_a0,
     author = {N. V. Bayanova and N. Ya. Medvedev},
     title = {Vector {Lattices} on {a~Set} of {Two} {Generators}},
     journal = {Algebra i logika},
     pages = {391--410},
     publisher = {mathdoc},
     volume = {41},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2002_41_4_a0/}
}
TY  - JOUR
AU  - N. V. Bayanova
AU  - N. Ya. Medvedev
TI  - Vector Lattices on a~Set of Two Generators
JO  - Algebra i logika
PY  - 2002
SP  - 391
EP  - 410
VL  - 41
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2002_41_4_a0/
LA  - ru
ID  - AL_2002_41_4_a0
ER  - 
%0 Journal Article
%A N. V. Bayanova
%A N. Ya. Medvedev
%T Vector Lattices on a~Set of Two Generators
%J Algebra i logika
%D 2002
%P 391-410
%V 41
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2002_41_4_a0/
%G ru
%F AL_2002_41_4_a0
N. V. Bayanova; N. Ya. Medvedev. Vector Lattices on a~Set of Two Generators. Algebra i logika, Tome 41 (2002) no. 4, pp. 391-410. http://geodesic.mathdoc.fr/item/AL_2002_41_4_a0/

[1] K. Baker, Topological methods in the algebraic theory of vector lattices, Doctoral Dissertation, Harvard University, 1966

[2] K. Baker, “Free vector lattices”, Can. J. Math., 20:1 (1968), 58–66 | MR | Zbl

[3] M. Darnel, “The structure of free abelian $l$-groups and free vector lattices”, Algebra Univers., 23:2 (1986), 99–110 | DOI | MR | Zbl

[4] V. M. Kopytov, Reshetochno uporyadochennye gruppy, Nauka, M., 1984 | MR | Zbl

[5] M. I. Kargapolov, Yu. I. Merzlyakov, Teoriya grupp, Nauka, M., 1977 | MR | Zbl

[6] R. Bleier, “Archimedean vector lattices generated by two elements”, Proc. Am. Math. Soc., 39:1 (1973), 1–9 | DOI | MR | Zbl

[7] W. Beynon, “Duality theorems for finitely generated vector lattices”, Proc. Lond. Math. Soc.(III), 31:1 (1975), 114–128 | DOI | MR | Zbl

[8] R. Bleier, “Free vector lattices”, Trans. Am. Math. Soc., 176:1 (1973), 73–87 | DOI | MR | Zbl

[9] G. Birkgof, Teoriya reshetok, Nauka, M., 1984 | MR

[10] D. Kenoyer, “Recognizability in the lattice of convex $l$-subgroups in the latticeordered groups”, Czech. Math. J., 109:34 (1984), 411–416 | MR | Zbl

[11] K. Yosida, “On a vector lattice with unit”, Proc. Japan Acad., 17:1 (1941), 121–124 | MR | Zbl

[12] D. Madden, “$l$-groups of piecewise linear functions”, Ordered Algebraic Structures, Lect. Notes Pure Appl. Math., 99, Marcel Dekker, New York, 1985, 117–124 | MR

[13] P. Conrad, “Torsion radicals of lattice-ordered groups”, Gruppi e anelli ordinati (Convegno 1975), Symp. Math., 21, Academic Press, London, 1977, 479–513 | MR