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18 relations: Algebraic structure, American Mathematical Society, Category theory, CRC Press, Empty set, Field with one element, Function (mathematics), Identity element, Initial and terminal objects, Inverse semigroup, Mathematics, Monoid, Semigroup, Semigroup with three elements, Semigroup with two elements, Special classes of semigroups, Trivial semigroup, Vacuous truth.
Algebraic structure
In mathematics, and more specifically in abstract algebra, an algebraic structure on a set A (called carrier set or underlying set) is a collection of finitary operations on A; the set A with this structure is also called an algebra.
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American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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Category theory
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
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CRC Press
The CRC Press, LLC is a publishing group based in the United States that specializes in producing technical books.
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Empty set
In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
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Field with one element
In mathematics, the field with one element is a suggestive name for an object that should behave similarly to a finite field with a single element, if such a field could exist.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Identity element
In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.
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Initial and terminal objects
In category theory, a branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely one morphism I → X. The dual notion is that of a terminal object (also called terminal element): T is terminal if for every object X in C there exists a single morphism X → T. Initial objects are also called coterminal or universal, and terminal objects are also called final.
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Inverse semigroup
In group theory, an inverse semigroup (occasionally called an inversion semigroup) S is a semigroup in which every element x in S has a unique inverse y in S in the sense that x.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Monoid
In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element.
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Semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation.
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Semigroup with three elements
In abstract algebra, a semigroup with three elements is an object consisting of three elements and an associative operation defined on them.
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Semigroup with two elements
In mathematics, a semigroup with two elements is a semigroup for which the cardinality of the underlying set is two.
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Special classes of semigroups
In mathematics, a semigroup is a nonempty set together with an associative binary operation.
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Trivial semigroup
In mathematics, a trivial semigroup (a semigroup with one element) is a semigroup for which the cardinality of the underlying set is one.
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Vacuous truth
In mathematics and logic, a vacuous truth is a statement that asserts that all members of the empty set have a certain property.
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