On generators of commutative semifields
V\'it\v{e}zslav Kala, Lucien \v{S}\'ima
TL;DR
This paper classifies ideal-simple commutative semirings, especially semifields, and shows that their minimal number of generators increases linearly with the depth of an associated rooted forest.
Contribution
It provides a classification of ideal-simple commutative semirings and establishes a linear growth relation for generators in semifields based on forest depth.
Findings
Classification of ideal-simple commutative semirings
Linear growth of minimal generators in semifields
Connection between generators and rooted forest depth
Abstract
We study ideal-simple commutative semirings and summarize the results giving their classification, in particular when they are finitely generated. In the principal case of (para)semifields, we then consider their minimal number of generators and show that it grows linearly with the depth of an associated rooted forest.
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Taxonomy
TopicsRings, Modules, and Algebras · Commutative Algebra and Its Applications · Scheduling and Optimization Algorithms