Identities of the stylic monoid

TL;DR

This paper establishes that the identities of stylic monoids with n generators match those of other well-studied monoids, solving the finite basis problem for stylic monoids.

Contribution

It proves that stylic monoids' identities coincide with those of certain known monoids, resolving the finite basis problem for these structures.

Findings

Identities of stylic monoids match those of Catalan and Kiselman monoids.

Finite basis problem is solved for stylic monoids.

Provides a unified understanding of identities across different monoid classes.

Abstract

We observe that for each $n\ge 2$, the identities of the stylic monoid with $n$ generators coincide with the identities of $n$-generated monoids from other distinguished series of $\mathscr{J}$-trivial monoids studied in the literature, e.g., Catalan monoids and Kiselman monoids. This solves the Finite Basis Problem for stylic monoids.