Difference between revisions of "Algebra"
From Encyclopedia of Mathematics
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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]]. | |
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. | 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. | ||
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]]). | 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]]). | ||
Revision as of 14:28, 13 January 2012
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.
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. (cf. Boolean algebra; Unary algebra).
How to Cite This Entry:
Algebra. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Algebra&oldid=20269
Algebra. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Algebra&oldid=20269