Arithmetic of Semigroup Semirings

  • V. Ponomarenko

Abstract

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.
Published
25.02.2015
How to Cite
Ponomarenko, V. “Arithmetic of Semigroup Semirings”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 2, Feb. 2015, pp. 213-29, http://umj.imath.kiev.ua/index.php/umj/article/view/1975.
Section
Research articles