FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 1, PAGES 93-119

**The prime ($RI$*-decidable) radical of
the unitary group over a ring with involution**

A. Yu. Golubkov

Abstract

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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.
```

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Last modified: April 11, 2000