FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 5, PAGES 55-68

**On $l$-prime radicals of lattice ordered
algebras**

J. V. Kochetova

Abstract

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The Kopytov order for any algebras over a field is considered.
The purpose of this paper is to investigate a generalization of
the concept of prime radical to lattice ordered algebras over
partially ordered fields.
Prime radicals of $l$-algebras over partially
ordered and directed fields are described.
Some results concerning properties of the lower weakly solvable
$l$-radical of
$l$-algebras are
obtained.
Necessary and sufficient conditions for the $l$-prime radical of an
$l$-algebra to be
equal to the lower weakly solvable $l$-radical of an $l$-algebra are presented.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k115/k11503h.htm

Last modified: October 18, 2012