Primary and strongly primary monoids and domains play a central role in the ideal and
factorization theory of commutative monoids and domains. It is well-known that primary …

We study some of the factorization invariants of the class of Puiseux monoids generated by
geometric sequences, and we compare and contrast them with the known results for …

A Puiseux monoid is an additive submonoid of the nonnegative rational numbers. If M is a
Puiseux monoid, then the question of whether each nonunit element of M can be written as a …

Nonunique factorization in commutative monoids is often studied using factorization
invariants, which assign to each monoid element a quantity determined by the factorization …

Problems involving chains of irreducible factorizations in atomic integral domains and
monoids have been the focus of much recent literature. If S is a commutative cancellative …

Arithmetical invariants—such as sets of lengths, catenary and tame degrees—describe the
non-uniqueness of factorizations in atomic monoids. We study these arithmetical invariants …

In an atomic, cancellative, commutative monoid S, the elasticity of an element provides a
coarse measure of its non-unique factorizations by comparing the largest and smallest …

We study the sets of lengths and unions of sets of lengths of numerical monoids. Our paper
focuses on a numerical monoid S generated by an arithmetic progression of positive …

We construct an algorithm which computes the catenary and tame degree of a numerical
monoid. As an example we explicitly calculate the catenary and tame degree of numerical …

Transfer Krull monoids are monoids which allow a weak transfer homomorphism to a
commutative Krull monoid, and hence the system of sets of lengths of a transfer Krull monoid …