On strongly primary monoids, with a focus on Puiseux monoids
By Alfred Geroldinger, Felix Gotti, S. Tringali. Journal of Algebra, 2019
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Primary and strongly primary monoids and domains play a central role in the ideal and factorization theory of commutative monoids and domains. Among others, it is known that primary monoids satisfying the ascending chain condition on divisorial ideals (e.g., numerical monoids) are strongly primary; and the multiplicative monoid of non-zero elements of a one-dimensional local domain is primary and it is strongly primary if the domain is noetherian. In the present paper, we focus on the study of additive submonoids of the non-negative rationals, called Puiseux monoids. It is easy to see that Puiseux monoids are primary monoids, and we provide conditions ensuring that they are strongly primary. Then we study local and global tameness of strongly primary Puiseux monoids; most notably, we establish an algebraic characterization of when a Puiseux monoid is globally tame. Moreover, we obtain a result on the structure of sets of lengths of all locally tame strongly primary monoids.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/297c9dd34f9c0bbae35fb67a523f1821f9ef89e5
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In Algebra and Number Theory
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- Factorization theory in commutative monoids (2019, background): “if Hb is a valuation monoid. 3. There is M ∈ N 0 such that every L ∈ L(H) is a finite AAP with difference min∆(H) and bound M. Proof. 1. and 3. follow from [42, Theorems 3.1.1 and 4.3.6] and for 2. see [41]. Now we consider the global case. Weakly Krull domains were introduced by Anderson, Anderson, M”