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Algebraic structure and Exponentiation

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Algebraic structure and Exponentiation

Algebraic structure vs. Exponentiation

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. Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.

Similarities between Algebraic structure and Exponentiation

Algebraic structure and Exponentiation have 23 things in common (in Unionpedia): Abelian group, Abstract algebra, Addition, Associative property, Binary operation, Commutative property, Direct sum of modules, Field (mathematics), Function (mathematics), Group (mathematics), Identity element, Infinite set, Inverse element, Magma (algebra), Mathematical structure, Mathematics, Monoid, Multiplication, Operation (mathematics), Ring (mathematics), Set (mathematics), Set 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.

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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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Addition

Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.

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Associative property

In mathematics, the associative property is a property of some binary operations.

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Binary operation

In mathematics, a binary operation on a set is a calculation that combines two elements of the set (called operands) to produce another element of the set.

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Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

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Direct sum of modules

In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module.

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Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

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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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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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Infinite set

In set theory, an infinite set is a set that is not a finite set.

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Inverse element

In abstract algebra, the idea of an inverse element generalises concepts of a negation (sign reversal) in relation to addition, and a reciprocal in relation to multiplication.

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Magma (algebra)

In abstract algebra, a magma (or groupoid; not to be confused with groupoids in category theory) is a basic kind of algebraic structure.

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Mathematical structure

In mathematics, a structure on a set is an additional mathematical object that, in some manner, attaches (or relates) to that set to endow it with some additional meaning or significance.

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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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Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.

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Operation (mathematics)

In mathematics, an operation is a calculation from zero or more input values (called operands) to an output value.

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Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

Algebraic structure and Ring (mathematics) · Exponentiation and Ring (mathematics) · See more »

Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

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Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

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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.

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The list above answers the following questions

Algebraic structure and Exponentiation Comparison

Algebraic structure has 144 relations, while Exponentiation has 266. As they have in common 23, the Jaccard index is 5.61% = 23 / (144 + 266).

References

This article shows the relationship between Algebraic structure and Exponentiation. To access each article from which the information was extracted, please visit:

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