Arithmetic of Semigroup Semirings
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.
English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 2, pp 243-266.
Citation Example: Ponomarenko V. Arithmetic of Semigroup Semirings // Ukr. Mat. Zh. - 2015. - 67, № 2. - pp. 213-229.