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