Semigroup Theory

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6 domain-specific abstractions whose origin domain is Semigroup Theory.

• Biordered set — An abstract set of idempotent-like elements equipped with compatible left and right quasiorders and partial basic products that axiomatize the idempotent structure of a semigroup.
• Compact semigroup — A semigroup whose solution sets for arbitrary systems of word equations are already determined by some finite subsystem, under the algebraic compactness convention.
• Epigroup — A semigroup in which every element is group-bound: some positive power of it lies in a subgroup of the semigroup.
• Nilsemigroup — A semigroup with a zero element in which every individual element has some positive power equal to zero.
• Nowhere commutative semigroup — A semigroup in which two elements commute only when they are equal.
• Symmetric inverse semigroup — The inverse monoid of all partial bijections on a set under composition.