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On linearly ordered linear algebras

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Abstract

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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Authors and Affiliations

  1. Moscow State Pedagogical University, Moscow, Russia

    J. V. Kochetova & E. E. Shirshova

Authors
  1. J. V. Kochetova
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  2. E. E. Shirshova
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Correspondence to J. V. Kochetova.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 15, No. 1, pp. 53–63, 2009.

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Kochetova, J.V., Shirshova, E.E. On linearly ordered linear algebras. J Math Sci 166, 725–732 (2010). https://doi.org/10.1007/s10958-010-9888-y

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  • DOI: https://doi.org/10.1007/s10958-010-9888-y

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