Geodesic
Invariant subrings of induced rings
Izvestiya. Mathematics , Tome 4 (1970) no. 1, pp. 85-90.

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We study the invariant subrings of a certain class of induced rings. The result we obtain gives, in particular, an answer to a problem posed in $({}^1)$ concerning the structure of the invariant subrings of a ring that arises in the reduction, modulo a prime, of modular functions. 
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B. Kh. Kirshtein; I. I. Pyatetskii-Shapiro. Invariant subrings of induced rings. Izvestiya. Mathematics , Tome 4 (1970) no. 1, pp. 85-90. http://geodesic.mathdoc.fr/item/IM2_1970_4_1_a4/

[1] Pyatetskii-Shapiro I. I., “O reduktsii po prostomu modulyu polei modulyarnykh funktsii”, Izv. AN SSSR. Ser. matem., 32 (1968), 1264–1274