Geodesic
Rings of definition of dense subgroups of semisimple linear groups
Izvestiya. Mathematics , Tome 5 (1971) no. 1, pp. 45-55.

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We investigate the question: What is the smallest ring over which the elements of a dense subgroup (in the Zariski topology) of a emisimple algebraic group can be written down simultaneously for various rational linear representations? 
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È. B. Vinberg. Rings of definition of dense subgroups of semisimple linear groups. Izvestiya. Mathematics , Tome 5 (1971) no. 1, pp. 45-55. http://geodesic.mathdoc.fr/item/IM2_1971_5_1_a2/

[1] Zarisskii O., Samyuel P., Kommutativnaya algebra, t. 1,2, IL, M., 1963

[2] Vinberg E. B., “Diskretnye gruppy, porozhdennye otrazheniyami, v prostranstvakh Lobachevskogo”, Matem. sb., 72(114) (1967), 471–488 | MR | Zbl