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Arithmetic of Semigroup Semirings

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We define semigroup semirings by analogy with group rings and semigroup rings. We study the arithmetic properties and determine sufficient conditions under which a semigroup semiring is atomic, has finite factorization, or has bounded factorization. We also present a semigroup-semiring analog (although not a generalization) of the Gauss lemma on primitive polynomials.

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Author information

Correspondence to V. Ponomarenko.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 2, pp. 213–229, February, 2015.

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Ponomarenko, V. Arithmetic of Semigroup Semirings. Ukr Math J 67, 243–266 (2015). https://doi.org/10.1007/s11253-015-1077-1

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Keywords

  • Group Ring
  • Semigroup Forum
  • Unique Factorization
  • Great Common Divisor
  • Commutative Semigroup