Factorizations in evaluation monoids of Laurent semirings

Abstract

For let be the semiring of real numbers with all where is the set of nonnegative integers and is the semiring of Laurent polynomials with coefficients in In this paper, we study various factorization properties of the additive structure of We characterize when is atomic. Then we characterize when satisfies the ascending chain condition on principal ideals in terms of certain well-studied factorization properties. Finally, we characterize when satisfies the unique factorization property and show that, when this is not the case, has infinite elasticity.