Complexity Degrees of Algebraic Structures

TL;DR

This paper introduces a novel approach to measuring the complexity of algebraic structures over commutative rings using multiplicity theory, providing new insights into their construction and properties.

Contribution

It presents a new method for assigning size measures to algebraic structures and their constructions, advancing the understanding of their complexity.

Findings

Develops a multiplicity-based complexity measure for algebraic structures

Analyzes the complexity of algebraic constructions over commutative rings

Provides a framework for comparing algebraic structures based on their complexity

Abstract

We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity theory, to the algebras and to the construction itself is a novel aspect to the subject.