Applications of the Graph Minor Theorem to algebraic structures I

TL;DR

This paper applies the Graph Minor Theorem to characterize infinite sequences of finite subsets within factorial and commutative semigroups, providing new insights into their structural properties.

Contribution

It introduces a novel application of the Graph Minor Theorem to algebraic structures, specifically to classify sequences in factorial and commutative semigroups.

Findings

Characterization of infinite sequences in factorial semigroups

Application of Graph Minor Theorem to algebraic structures

Insights into the structure of semigroups with a unity element

Abstract

We use the Graph Minor Theorem to characterize infinite sequences of finite subsets of factorial and commutative semigroups (here semigroups have a unity element), e.g. the multiplicative semigroup of a unique factorization domain.