FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 1, PAGES 53-63

On linearly ordered linear algebras

J. V. Kochetova
E. E. Shirshova

Abstract

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The Kopytov order for any algebras 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.

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Last modified: December 2, 2009