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24 relations: Absorbing element, Algebraic structure, American Mathematical Society, Cardinality, Category theory, Cayley table, Counterexample, CRC Press, Distinct (mathematics), Empty semigroup, Field with one element, Group (mathematics), Identity element, Initial and terminal objects, Isomorphism, Mathematics, Semigroup, Semigroup with three elements, Semigroup with two elements, Special classes of semigroups, Structure, Trivial group, Zero ring, 1.
Absorbing element
In mathematics, an absorbing element is a special type of element of a set with respect to a binary operation on that set.
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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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Cardinality
In mathematics, the cardinality of a set is a measure of the "number of elements of the set".
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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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Cayley table
A Cayley table, after the 19th century British mathematician Arthur Cayley, describes the structure of a finite group by arranging all the possible products of all the group's elements in a square table reminiscent of an addition or multiplication table.
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Counterexample
In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule or law.
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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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Distinct (mathematics)
In mathematics, two things are called distinct if they are not equal.
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Empty semigroup
In mathematics, a semigroup with no elements (the empty semigroup) is a semigroup in which the underlying set is the empty set.
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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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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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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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Isomorphism
In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.
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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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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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Structure
Structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized.
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Trivial group
In mathematics, a trivial group is a group consisting of a single element.
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Zero ring
In ring theory, a branch of mathematics, the zero ring or trivial ring is the unique ring (up to isomorphism) consisting of one element.
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1
1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph.
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Semigroup with 1 elements, Semigroup with one element.
References
[1] https://en.wikipedia.org/wiki/Trivial_semigroup
