Factorization in additive monoids of evaluation polynomial semirings
Name
Factorization in additive monoids of evaluation polynomial semirings.pdf
Description
Published version
Size
1.63 MB
Format
Adobe PDF
Checksum (MD5)
e877f97be759cc23f34d78e92d92aaa8
Author(s)
Ajran, Khalid
Bringas, Juliet
Li, Bangzheng
Singer, Easton
Tirador, Marcos
Date Issued
June 1, 2023
Journal
Communications in Algebra
Publisher
Taylor & Francis
Citation
Ajran, K., Bringas, J., Li, B., Singer, E., & Tirador, M. (2023). Factorization in additive monoids of evaluation polynomial semirings. Communications in Algebra, 51(10), 4347–4362.
Version
Final published version
Abstract
For a positive real α, we can consider the additive submonoid M of the real line that is generated by the nonnegative powers of α. When α is transcendental, M is a unique factorization monoid. However, when α is algebraic, M may not be atomic, and even when M is atomic, it may contain elements having more than one factorization (i.e., decomposition as a sum of irreducibles). The main purpose of this paper is to study the phenomenon of multiple factorizations inside M. When α is algebraic but not rational, the arithmetic of factorizations in M is highly interesting and complex. In order to arrive to that conclusion, we investigate various factorization invariants of M, including the sets of lengths, sets of Betti elements, and catenary degrees. Our investigation gives continuity to recent studies carried out by Chapman et al. in 2020 and by Correa-Morris and Gotti in 2022.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1080/00927872.2023.2208672
