Endomorphism ring and Vector space

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Difference between Endomorphism ring and Vector space

Endomorphism ring vs. Vector space

In abstract algebra, the endomorphism ring of an abelian group X, denoted by End(X), is the set of all endomorphisms of X (i.e., the set of all homomorphisms of X into itself) endowed with an addition operation defined by pointwise addition of functions and a multiplication operation defined by function composition. 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.

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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Addison-Wesley

Addison-Wesley is a publisher of textbooks and computer literature.

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Associative property

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

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Category (mathematics)

In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is an algebraic structure similar to a group but without requiring inverse or closure properties.

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Division ring

In abstract algebra, a division ring, also called a skew field, is a ring in which division is possible.

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Endomorphism

In mathematics, an endomorphism is a morphism (or homomorphism) from a mathematical object to itself.

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Free module

In mathematics, a free module is a module that has a basis – that is, a generating set consisting of linearly independent elements.

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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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Function composition

In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.

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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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Identity function

Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.

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Module (mathematics)

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

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Projective module

In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, by keeping some of the main properties of free modules.

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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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