TL;DR
This paper offers concise proofs of classical theorems related to idempotent generated semigroups of transformations on finite sets, simplifying existing complex proofs.
Contribution
It introduces streamlined proofs for foundational theorems in the theory of idempotent generated semigroups of transformations.
Findings
Simplified proofs of classical theorems
Clarification of properties of idempotent generated semigroups
Enhanced understanding of transformation semigroups
Abstract
We provide short and direct proofs for some classical theorems proved by Howie, Levi and McFadden concerning idempotent generated semigroups of transformations on a finite set.
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