Geodesic
The prime ($RI^*$-decidable) radical of the~unitary group over a~ring with involution
Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 1, pp. 93-119

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We establish a connection between the $RI^*$-decidable radical of the unitary group and the prime radical of a ring for the case of an associative ring with involution and $1/2$ containing a suitable system of elements analogous to elementary matrices. We demonstrate the connection between existence of a decidable radical of the unitary group and nilpotency of the prime radical of a ring. 
@article{FPM_2000_6_1_a8,
     author = {A. Yu. Golubkov},
     title = {The prime ($RI^*$-decidable) radical of the~unitary group over a~ring with involution},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {93--119},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2000_6_1_a8/}
}
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A. Yu. Golubkov. The prime ($RI^*$-decidable) radical of the~unitary group over a~ring with involution. Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 1, pp. 93-119. http://geodesic.mathdoc.fr/item/FPM_2000_6_1_a8/