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Cyclic semirings with idempotent noncommutative addition

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Abstract

The article discusses the structure of cyclic semirings with noncommutative addition. In the infinite case, the addition is idempotent and is either left or right. Addition of a finite cyclic semirings can be either idempotent or nonidempotent. In the finite additively idempotent cyclic semiring, addition is reduced to the addition of a cyclic subsemiring with commutative addition and an absorbing element for multiplication and the addition of a cycle that is a finite semifield.

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Authors and Affiliations

  1. Vyatka State University of Humanities, Vyatka, Russia

    E. M. Vechtomov & I. V. Lubyagina

Authors
  1. E. M. Vechtomov
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  2. I. V. Lubyagina
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Correspondence to E. M. Vechtomov.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 1, pp. 33–52, 2011/12.

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Vechtomov, E.M., Lubyagina, I.V. Cyclic semirings with idempotent noncommutative addition. J Math Sci 185, 367–380 (2012). https://doi.org/10.1007/s10958-012-0921-1

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  • DOI: https://doi.org/10.1007/s10958-012-0921-1

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