8 February 2024
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
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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