Journal of Commutative Algebra
- J. Commut. Algebra
- Volume 12, Number 3 (2020), 319-331.
The elasticity of Puiseux monoids
Let be an atomic monoid and let be a non-unit element of . The elasticity of , denoted by , is the ratio of its largest factorization length to its shortest factorization length, and it measures how far is from having all its factorizations of the same length. The elasticity of is the supremum of the elasticities of all non-unit elements of . In this paper, we study the elasticity of Puiseux monoids (i.e., additive submonoids of ). We characterize, in terms of the atoms, which Puiseux monoids have finite elasticity, giving a formula for in this case. We also classify when is achieved by an element of . When is a primary Puiseux monoid (that is, a Puiseux monoid whose atoms have prime denominator), we describe the topology of the set of elasticities of , including a characterization of when is a bounded factorization monoid. Lastly, we give an example of a Puiseux monoid that is bifurcus (that is, every nonzero element has a factorization of length at most ).
J. Commut. Algebra, Volume 12, Number 3 (2020), 319-331.
Received: 24 March 2017
Revised: 1 December 2017
Accepted: 17 December 2017
First available in Project Euclid: 5 September 2020
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Gotti, Felix; O’Neill, Christopher. The elasticity of Puiseux monoids. J. Commut. Algebra 12 (2020), no. 3, 319--331. doi:10.1216/jca.2020.12.319. https://projecteuclid.org/euclid.jca/1599271221