I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2009, VOLUME 15, NUMBER 1, PAGES 157-173
Special classes of -rings
N. E. Shavgulidze
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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 -ring is equal to the
intersection of the right -prime -ideals for each of which
the following condition holds: the quotient -ring by the maximal
contained in a given right -ideal belongs to the
The prime radical of an -ring is equal to the
intersection of the right -semiprime -ideals.
We introduce the notion of a completely -prime -ideal.
We prove that is equal
to the intersection of the completely -prime, right -ideals of an -ring , where is the
special radical of the -ring defined by the class of
positive divisors of zero.
Last modified: December 2, 2009