On strongly primary monoids, with a focus on Puiseux monoids

Primary and strongly primary monoids domains play a central role in the ideal factorization theory of commutative domains. It is well-known that satisfying ascending chain condition on divisorial ideals (e.g., numerical monoids) are primary; multiplicative monoid non-zero elements one-dimensional local domain it if Noetherian. In present paper, we focus study additive submonoids non-negative rationals, called Puiseux monoids. easy to see monoids, provide conditions ensuring they primary. Then global tameness monoids; most notably, establish an algebraic characterization when globally tame. Moreover, obtain result structure sets lengths all locally tame