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

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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},
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     publisher = {mathdoc},
     volume = {41},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2002_41_4_a0/}
}
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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/