Abstract
We say that a Puiseux monoid is exponential provided that it is generated by some of the powers of a rational number. Here we study the atomic properties of exponential Puiseux monoids and semirings. First, we characterize atomic exponential Puiseux monoids, and we prove that the finite factorization property, the bounded factorization property, and the ACCP coincide in this context. Then we proceed to offer necessary and sufficient conditions for an exponential Puiseux monoid to satisfy the ACCP. We conclude by describing the exponential Puiseux monoids that are semirings.
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