Faster access than browser!Similarities between Automorphism and Field (mathematics)
Automorphism and Field (mathematics) have 29 things in common (in Unionpedia): Abelian group, Algebra over a field, Algebraic structure, Associative property, Axiom of choice, Bijection, Class (set theory), Complex number, Continuous function, Field extension, Frobenius endomorphism, Galois extension, Galois group, Group (mathematics), Integer, Isomorphism, Linear algebra, Mathematics, Octonion, Quaternion, Rational number, Real number, Ring (mathematics), Ring homomorphism, Subgroup, Symmetric group, Uncountable set, Unit (ring theory), Vector space.
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.
Abelian group and Automorphism · Abelian group and Field (mathematics) ·
Algebra over a field
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.
Algebra over a field and Automorphism · Algebra over a field and Field (mathematics) ·
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.
Algebraic structure and Automorphism · Algebraic structure and Field (mathematics) ·
Associative property
In mathematics, the associative property is a property of some binary operations.
Associative property and Automorphism · Associative property and Field (mathematics) ·
Axiom of choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty.
Automorphism and Axiom of choice · Axiom of choice and Field (mathematics) ·
Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
Automorphism and Bijection · Bijection and Field (mathematics) ·
Class (set theory)
In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share.
Automorphism and Class (set theory) · Class (set theory) and Field (mathematics) ·
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.
Automorphism and Complex number · Complex number and Field (mathematics) ·
Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
Automorphism and Continuous function · Continuous function and Field (mathematics) ·
Field extension
In mathematics, and in particular, algebra, a field E is an extension field of a field F if E contains F and the operations of F are those of E restricted to F. Equivalently, F is a subfield of E. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers.
Automorphism and Field extension · Field (mathematics) and Field extension ·
Frobenius endomorphism
In commutative algebra and field theory, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of commutative rings with prime characteristic, an important class which includes finite fields.
Automorphism and Frobenius endomorphism · Field (mathematics) and Frobenius endomorphism ·
Galois extension
In mathematics, a Galois extension is an algebraic field extension E/F that is normal and separable; or equivalently, E/F is algebraic, and the field fixed by the automorphism group Aut(E/F) is precisely the base field F. The significance of being a Galois extension is that the extension has a Galois group and obeys the fundamental theorem of Galois theory.
Automorphism and Galois extension · Field (mathematics) and Galois extension ·
Galois group
In mathematics, more specifically in the area of abstract algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension.
Automorphism and Galois group · Field (mathematics) and Galois group ·
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.
Automorphism and Group (mathematics) · Field (mathematics) and Group (mathematics) ·
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").
Automorphism and Integer · Field (mathematics) and Integer ·
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.
Automorphism and Isomorphism · Field (mathematics) and Isomorphism ·
Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.
Automorphism and Linear algebra · Field (mathematics) and Linear algebra ·
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
Automorphism and Mathematics · Field (mathematics) and Mathematics ·
Octonion
In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold \mathbb O. There are three lower-dimensional normed division algebras over the reals: the real numbers R themselves, the complex numbers C, and the quaternions H. The octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension.
Automorphism and Octonion · Field (mathematics) and Octonion ·
Quaternion
In mathematics, the quaternions are a number system that extends the complex numbers.
Automorphism and Quaternion · Field (mathematics) and Quaternion ·
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.
Automorphism and Rational number · Field (mathematics) and Rational number ·
Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
Automorphism and Real number · Field (mathematics) and Real number ·
Ring (mathematics)
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
Automorphism and Ring (mathematics) · Field (mathematics) and Ring (mathematics) ·
Ring homomorphism
In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the structure.
Automorphism and Ring homomorphism · Field (mathematics) and Ring homomorphism ·
Subgroup
In group theory, a branch of mathematics, given a group G under a binary operation ∗, a subset H of G is called a subgroup of G if H also forms a group under the operation ∗.
Automorphism and Subgroup · Field (mathematics) and Subgroup ·
Symmetric group
In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.
Automorphism and Symmetric group · Field (mathematics) and Symmetric group ·
Uncountable set
In mathematics, an uncountable set (or uncountably infinite set) is an infinite set that contains too many elements to be countable.
Automorphism and Uncountable set · Field (mathematics) and Uncountable set ·
Unit (ring theory)
In mathematics, an invertible element or a unit in a (unital) ring is any element that has an inverse element in the multiplicative monoid of, i.e. an element such that The set of units of any ring is closed under multiplication (the product of two units is again a unit), and forms a group for this operation.
Automorphism and Unit (ring theory) · Field (mathematics) and Unit (ring theory) ·
Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
Automorphism and Vector space · Field (mathematics) and Vector space ·
The list above answers the following questions
- What Automorphism and Field (mathematics) have in common
- What are the similarities between Automorphism and Field (mathematics)
Automorphism and Field (mathematics) Comparison
Automorphism has 94 relations, while Field (mathematics) has 290. As they have in common 29, the Jaccard index is 7.55% = 29 / (94 + 290).
References
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