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Semigroup Green relation heights

Published on:

8 February 2024

Primary Category:

Combinatorics

Paper Authors:

Matthew Brookes,

Craig Miller

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Key Details

Explores heights of posets of Green's relations on semigroups

Focuses on stable semigroups, including all finite semigroups

Shows for these semigroups, finite L-height implies finite R- and J-heights

Provides tight upper bounds on R- and J-heights based on L-height

Constructs examples realizing all possible height combinations

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Semigroup Green relation heights

This paper explores heights of posets formed by Green's relations on semigroups. It focuses on stable semigroups, proving equalities between L-, R-, J- and H-heights. Main results: for a stable semigroup with L-height n, the R-height and J-height are between n and 2^n - 1, with examples realizing these bounds. Also if L- and R-heights are at least 2, the J-height is bounded by their sum minus 2.

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