Geodesic
On closeness of carpets of Lie type over commutative rings
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 192-196

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For a wide class of commutative rings, the existence of non-closed irreducible carpets of Lie type associated with any root system is proved.
Keywords: chevalley group over a commutative ring, carpet of additive subgroups, carpet subgroup. 
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     title = {On closeness of carpets of {Lie} type over commutative rings},
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S. K. Kuklina; A. O. Likhacheva; Ya. N. Nuzhin. On closeness of carpets of Lie type over commutative rings. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 192-196. http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a20/