# Idempotent ordered semigroup

Source: [Idempotent ordered semigroup](<https://www.sota2.com/research/paper/68fa54031e209131ce988066>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T12:46:25.427Z

Authors: K. Hansda

Published: 2017-06-26T03:17:18.000Z

## Abstract

An element e of an ordered semigroup $(S,\\cdot,\\leq)$ is called an ordered idempotent if $e\\leq e^2$. We call an ordered semigroup $S$ idempotent ordered semigroup if every element of $S$ is an ordered idempotent. Every idempotent semigroup is a complete semilattice of rectangular idempotent semigroups and in this way we arrive to many other important classes of idempotent ordered semigroups.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1706.08213>)

[PDF](<https://arxiv.org/pdf/1706.08213.pdf>)