Free iterative and iteration K-semialgebras

TL;DR

This paper characterizes algebras of rational power series over a semiring as free algebras within certain algebraic classes, providing a foundational understanding of their structure.

Contribution

It introduces a new characterization of rational power series algebras as free objects in algebraic structures over a semiring.

Findings

Algebras of rational power series are identified as free in specific algebraic classes.

Provides a unifying framework for understanding these algebras in algebraic terms.

Enhances theoretical understanding of power series in algebraic structures.

Abstract

We consider algebras of rational power series over an alphabet $\Sigma$ with coefficients in a commutative semiring $K$ and characterize them as the free algebras in various classes of algebraic structures.