FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2013, VOLUME 18, NUMBER 1, PAGES 85-158

**Prime radicals of lattice $K$-ordered
algebras**

J. V. Kochetova

E. E. Shirshova

Abstract

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The Kopytov order for any algebra over a field is considered.
Necessary and sufficient conditions for an algebra to be
a linearly ordered algebra are presented.
Some results concerning the properties of ideals of linearly ordered
algebras are obtained.
Some examples of algebras with the Kopytov order are described.
The Kopytov order for these examples induces the order on other
algebraic objects.
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 the 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 the
$l$-algebra are
presented.

Location: http://mech.math.msu.su/~fpm/eng/k13/k131/k13108h.htm

Last modified: September 5, 2013