FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 8, PAGES 169-181

**Radicals of $l$-rings and one-sided
$l$-ideals**

N. E. Shavgulidze

Abstract

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In this paper, we introduce the notion of an $l$-prime $l$-ideal and that of
a right $l$-semiprime $l$-ideal.
We prove that our definitions coincide with the definitions of
M. A. Shatalova in the case of two-sided $l$-ideals.
Our main results are the following ones.
The radical of an $l$-ring can be represented
as the intersection of the right $l$-ideals for each of which
the following condition holds: the quotient ring by the maximal
$l$-ideal
contained in the given right $l$-ideal is semisimple.
The hypernilpotent radical of an $l$-ring can be represented
as the intersection of the right $l$-semiprime ideals
satisfying the same condition.

Location: http://mech.math.msu.su/~fpm/eng/k08/k088/k08811h.htm

Last modified: November 18, 2009