Primitive orthogonal idempotents for R-trivial monoids

TL;DR

This paper introduces a recursive method to construct primitive orthogonal idempotents for R-trivial monoids, leveraging a new equivalence with weakly ordered monoids to advance algebraic understanding.

Contribution

It provides the first recursive formula for primitive orthogonal idempotents in R-trivial monoids, based on a novel equivalence with weakly ordered monoids.

Findings

Recursive formula for idempotents derived

Established equivalence between R-trivial and weakly ordered monoids

Enhanced algebraic framework for R-trivial monoids

Abstract

We construct a recursive formula for a complete system of primitive orthogonal idempotents for any $R$-trivial monoid. This uses the newly proved equivalence between the notions of $R$-trivial monoid and weakly ordered monoid.