I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2008, VOLUME 14, NUMBER 8, PAGES 169-181
Radicals of -rings and one-sided
N. E. Shavgulidze
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In this paper, we introduce the notion of an -prime -ideal and that of
a right -semiprime -ideal.
We prove that our definitions coincide with the definitions of
M. A. Shatalova in the case of two-sided -ideals.
Our main results are the following ones.
The radical of an -ring can be represented
as the intersection of the right -ideals for each of which
the following condition holds: the quotient ring by the maximal
contained in the given right -ideal is semisimple.
The hypernilpotent radical of an -ring can be represented
as the intersection of the right -semiprime ideals
satisfying the same condition.
Last modified: November 18, 2009