FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 1, PAGES 157-173

**Special classes of $l$-rings**

N. E. Shavgulidze

Abstract

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We study a special class of lattice-ordered rings and
a special radical.
We prove that a special radical of an $l$-ring is equal to the
intersection of the right $l$-prime $l$-ideals for each of which
the following condition holds: the quotient $l$-ring by the maximal
$l$-ideal
contained in a given right $l$-ideal belongs to the
special class.
The prime radical of an $l$-ring is equal to the
intersection of the right $l$-semiprime $l$-ideals.
We introduce the notion of a completely $l$-prime $l$-ideal.
We prove that $N$_{3}(R) is equal
to the intersection of the completely $l$-prime, right $l$-ideals of an $l$-ring $R$, where $N$_{3}(R) is the
special radical of the $l$-ring $R$ defined by the class of
$l$-rings without
positive divisors of zero.

Location: http://mech.math.msu.su/~fpm/eng/k09/k091/k09112h.htm

Last modified: December 2, 2009