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Difference between revisions of "Algebra"

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'''Algebra''' is a branch of [[mathematics]]. The term is used in combinations such as [[Homological algebra|homological algebra]], [[Commutative algebra|commutative algebra]], [[Linear-algebra(2)|linear algebra]], [[Multilinear algebra|multilinear algebra]], and [[Topological algebra|topological algebra]].
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'''Algebra''' is a branch of [[mathematics]]. The term is used in combinations such as [[homological algebra]], [[commutative algebra]], [[Linear-algebra(2)|linear algebra]], [[multilinear algebra]], and [[topological algebra]].
  
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A special case of an [[Operator ring|operator ring]]: An algebra (occasionally, a linear or vector algebra) over a field, over a skew-field or over a commutative ring. Associative algebras (formerly described as  "hypercomplex systems" ) and non-associative algebras are algebras in this sense.
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An [[algebraic system]], consisting of a set with a family of algebraic operations.
  
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A synonym of [[Universal algebra|universal algebra]]. This includes algebras such as Boolean algebras, unary algebras, etc. (cf. [[Boolean algebra|Boolean algebra]]; [[Unary algebra|Unary algebra]]).
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A special case of an [[operator ring]]: An algebra (occasionally, a linear or vector algebra) over a field, over a skew-field or over a commutative ring. [[Associative algebra]]s (formerly described as  "hypercomplex systems" ) and [[Non-associative rings and algebras|non-associative algebras]] are algebras in this sense.
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A synonym of [[universal algebra]]. This includes algebras such as [[Boolean algebra]]s, [[unary algebra]]s, etc.
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[[Category:Algebra]]

Latest revision as of 11:22, 9 April 2017

Algebra is a branch of mathematics. The term is used in combinations such as homological algebra, commutative algebra, linear algebra, multilinear algebra, and topological algebra.

An algebraic system, consisting of a set with a family of algebraic operations.

A special case of an operator ring: An algebra (occasionally, a linear or vector algebra) over a field, over a skew-field or over a commutative ring. Associative algebras (formerly described as "hypercomplex systems" ) and non-associative algebras are algebras in this sense.

A synonym of universal algebra. This includes algebras such as Boolean algebras, unary algebras, etc.

How to Cite This Entry:
Algebra. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Algebra&oldid=30992
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