Factorization invariants of Puiseux monoids generated by geometric sequences

By Scott T. Chapman, Felix Gotti, Marly Gotti. Communications in Algebra, 2019

59 citations recorded by the source corpus.

Abstract 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 Sr are nicely generated, we are able to give detailed descriptions of many of their factorization invariants. One distinguishing characteristic of Sr 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 Sr.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/833df3844fbcbe9c8bfd094b188841e60b48663a

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In Algebra and Number Theory

1. S. Tringali
2. Felix Gotti
3. Alfred Geroldinger

Citations in the corpus

• On strongly primary monoids, with a focus on Puiseux monoids (2019, background): “These Puiseux monoids were recently studied in [53], where special emphasis was put on the structure of their sets of lengths (the case where |B| = 1 was previously investigated in [11]).”