Factorization invariants of the additive structure of exponential Puiseux semirings

Exponential Puiseux semirings are additive submonoids of [Formula: see text] generated by almost all the nonnegative powers a positive rational number, and they natural generalizations cyclic semirings. In this paper, we investigate some factorization invariants exponential briefly explore connections these properties with semigroup-theoretical invariants. Specifically, provide exact formulas to compute catenary degrees monoids show that minima maxima their sets distances always attained at Betti elements. Additionally, prove lengths atomic arithmetic progressions common bound, while unions progressions. We conclude providing various characterizations finite omega functions; in particular, completely describe them terms presentations.