Factorization invariants of Puiseux monoids generated by geometric sequences

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 numerical monoids generated by arithmetic sequences. The class we study here consists of all atomic monoids of the form , where...

Full description

Saved in:
Bibliographic Details
Published in:Communications in algebra 2020-01, Vol.48 (1), p.380-396
Main Authors: Chapman, Scott T., Gotti, Felix, Gotti, Marly
Format: Article
Language:English
Subjects:
Arithmetic
Catenary degree
Factorization
factorization invariants
factorization theory
Invariants
Monoids
Primary: 20M13
Puiseux monoids
realization theorem
Secondary: 06F05
set of distances
system of sets of lengths
tame degree
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 numerical monoids generated by arithmetic sequences. The class we study here consists of all atomic monoids of the form , where r is a positive rational. As the atomic monoids S r are nicely generated, we are able to give detailed descriptions of many of their factorization invariants. One distinguishing characteristic of S r is that all its sets of lengths are arithmetic sequences of the same distance, namely , where are such that and . We prove this, and then use it to study the elasticity and tameness of S r .
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2019.1646269