Geodesic
Constructive Matrix and Orderable Groups
Algebra i logika, Tome 43 (2004) no. 3, pp. 353-363

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We study into the relationship between constructivizations of an associative commutative ring $K$ with unity and constructivizations of matrix groups $GL_n(K)$ (general), $SL_n(K)$ (special), and $UT_n(K)$ (unitriangular) over $K$. It is proved that for $n\geqslant3$, a corresponding group is constructible iff so is $K$. We also look at constructivizations of ordered groups. It turns out that a torsion-free constructible Abelian group is orderly constructible. It is stated that the unitriangular matrix group $UT_n(K)$ over an orderly constructible commutative associative ring $K$ is itself orderly constructible. A similar statement holds also for finitely generated nilpotent groups, and countable free nilpotent groups.
Mots-clés : matrix group
Keywords: ordered group, constructivization, orderly constructive system. 
@article{AL_2004_43_3_a4,
     author = {V. A. Roman'kov and N. G. Khisamiev},
     title = {Constructive {Matrix} and {Orderable} {Groups}},
     journal = {Algebra i logika},
     pages = {353--363},
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2004_43_3_a4/}
}
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V. A. Roman'kov; N. G. Khisamiev. Constructive Matrix and Orderable Groups. Algebra i logika, Tome 43 (2004) no. 3, pp. 353-363. http://geodesic.mathdoc.fr/item/AL_2004_43_3_a4/