Arithmetic of Semigroup Semirings - Ponomarenko, V. (Ukrains’kyi Matematychnyi Zhurnal, 2015)
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.