Том 69
№ 7

All Issues

Arithmetic of Semigroup Semirings

Ponomarenko V.


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.