On the atoms of algebraic lattices arising in $q$-theory

TL;DR

This paper investigates the fundamental building blocks, called atoms, of algebraic lattices that appear in the context of q-theory related to finite semigroups, enhancing understanding of their structure.

Contribution

It identifies and characterizes many atoms within these algebraic lattices, providing new insights into their composition in q-theory.

Findings

Identified numerous atoms in algebraic lattices from q-theory.

Enhanced understanding of lattice structure in finite semigroup contexts.

Contributed to the theoretical framework of algebraic lattices in semigroup theory.

Abstract

We determine many of the atoms of the algebraic lattices arising in $\mathfrak{q}$-theory of finite semigroups.