The Addition Theorem for algebraic entropies induced by non-discrete length functions

TL;DR

This paper proves the Addition Theorem for algebraic entropies induced by non-discrete length functions on locally finite modules over rings, providing concrete examples and expanding the theoretical framework of algebraic entropy.

Contribution

It establishes the validity of the Addition Theorem for a new class of algebraic entropies induced by non-discrete length functions, with explicit examples.

Findings

Addition Theorem holds for algebraic entropies from non-discrete length functions

Provides concrete examples of non-discrete length functions and their entropies

Extends the theoretical understanding of algebraic entropy in module categories

Abstract

The validity of the Addition Theorem for algebraic entropies $\ent_L$ induced by non-discrete length functions $L$ on the category of locally $L$-finite modules over arbitrary rings is proved. Concrete examples of non-discrete length functions and their induced algebraic entropies are provided.