Ideal lattices of semigroup of doubly stochastic matrices

TL;DR

This paper investigates the structure of idempotents in the semigroup of doubly stochastic matrices, providing formulas, locating specific idempotents, and describing their generated ideals forming lattices.

Contribution

It introduces a method to find the number of idempotents and describes the lattice structure of idempotent generated ideals in these semigroups.

Findings

Number of idempotents in D_n determined

Idempotents located for D_3 and D_4

Idempotent generated ideals form lattices

Abstract

In this paper we illustrate the rule for finding number of idempotents in the doubly stochastic matrix $D_n$ and also locate the idempotents for the semigroups $D_3$ and $D_4$. Further describe idempotent generated ideals of these semigroups and it is shown that these idempotent generated ideals form lattices.