Standard elements of the lattice of monoid varieties

TL;DR

This paper fully classifies the standard elements within the lattice of monoid varieties, establishing that these are precisely the neutral elements, thereby clarifying the structure of this mathematical lattice.

Contribution

It provides a complete classification of standard elements in the lattice of monoid varieties, linking them directly to neutral elements for the first time.

Findings

Standard elements are exactly the neutral elements.

Complete classification of standard elements in the lattice.

Clarifies the structure of the lattice of monoid varieties.

Abstract

We completely classify all standard elements in the lattice of all monoid varieties. In particular, we prove that an element of this lattice is standard if and only if it is neutral.