Computations of atom spectra

TL;DR

This paper introduces a method to explicitly compute the atom spectrum of module categories over various non-commutative rings, advancing the theoretical framework of atoms in abelian categories.

Contribution

It provides a practical computational approach for atom spectra in non-commutative settings, building on Kanda's theoretical work.

Findings

Method enables explicit computation of atom spectra

Applied to multiple examples demonstrating effectiveness

Advances understanding of atoms in non-commutative algebra

Abstract

This is a contribution to the theory of atoms in abelian categories recently developed in a series of papers by Kanda. We present a method that enables one to explicitly compute the atom spectrum of the module category over a wide range of non-commutative rings. We illustrate our method and results by several examples.