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