2017/12/03 by Gotti, Marly
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1712.00837
If M is an atomic monoid and x is a nonzero non-unit element of M, then the set of lengths L(x) of x is the set of all possible lengths of factorizations of x, where the length of a factorization is the number of irreducible factors (counting repetitions). In a recent paper, F. Gotti and C. O'Neil studied the sets of elasticities R(P) := \sup L(x)/inf L(x) : x ∈ P\ of Puiseux monoids P. Here we take this study a step forward and explore the local k-elasticities of the same class of monoids. We find conditions under which Puiseux monoids have all their local elasticities finite as well as conditions under which they have infinite local k-elasticities for sufficiently large k. Finally, we focus our study of the k-elasticities on the class of primary Puiseux monoids, proving that they have finite local k-elasticities if either they are boundedly generated and do not have any stable atoms or if they do not contain 0 as a limit point.