Relational depth is defined for chain J-class semigroups and exactly determined for ideals in the full transformation monoid, symmetric inverse monoid, and partial transformation monoid.
Howie, Fundamentals of Semigroup Theory, Clarendon Press, Oxford
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Relational depth of transformation semigroups and their ideals
Relational depth is defined for chain J-class semigroups and exactly determined for ideals in the full transformation monoid, symmetric inverse monoid, and partial transformation monoid.