On the factorization invariants of arithmetical congruence monoids

TL;DR

This paper investigates key factorization invariants such as catenary degree, length density, and omega primality within arithmetical congruence monoids, providing insights into their algebraic structure.

Contribution

It introduces a detailed analysis of factorization invariants in arithmetical congruence monoids, expanding understanding of their algebraic properties.

Findings

Determined bounds for the catenary degree in these monoids.

Characterized the distribution of factorization lengths.

Measured the omega primality to assess primality deviations.

Abstract

In this paper, we study various factorization invariants of arithmetical congruence monoids. The invariants we investigate are the catenary degree, a measure of the maximum distance between any two factorizations of the same element, the length density, which describes the distribution of the factorization lengths of an element, and the omega primality, which measures how far an element is from being prime.