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20 relations: Abelian group, Absolute value, Abstract algebra, Additive inverse, American Mathematical Society, Arithmetic, Closure (mathematics), Complex number, Identity element, Integer, Linearly ordered group, Negative number, Ordered field, Partially ordered ring, Rational number, Real number, Ring (mathematics), Total order, Zero divisor, Zero ring.
Abelian group
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.
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Absolute value
In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.
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Abstract algebra
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
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Additive inverse
In mathematics, the additive inverse of a number is the number that, when added to, yields zero.
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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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Arithmetic
Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.
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Closure (mathematics)
A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set; in this case we also say that the set is closed under the operation.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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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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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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Linearly ordered group
In abstract algebra a linearly ordered or totally ordered group is a group G equipped with a total order "≤", that is translation-invariant.
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Negative number
In mathematics, a negative number is a real number that is less than zero.
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Ordered field
In mathematics, an ordered field is a field together with a total ordering of its elements that is compatible with the field operations.
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Partially ordered ring
In abstract algebra, a partially ordered ring is a ring (A, +, ·), together with a compatible partial order, i.e. a partial order \leq on the underlying set A that is compatible with the ring operations in the sense that it satisfies: and for all x, y, z\in A. Various extensions of this definition exist that constrain the ring, the partial order, or both.
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Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Ring (mathematics)
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
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Total order
In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation on some set X, which is antisymmetric, transitive, and a connex relation.
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Zero divisor
In abstract algebra, an element of a ring is called a left zero divisor if there exists a nonzero such that, or equivalently if the map from to that sends to is not injective.
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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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