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- Supercommutative_algebra abstract "In mathematics, a supercommutative algebra is a superalgebra (i.e. a Z2-graded algebra) such that for any two homogeneous elements x, y we haveEquivalently, it is a superalgebra where the supercommutatoralways vanishes. Algebraic structures which supercommute in the above sense are sometimes referred to as skew-commutative associative algebras to emphasize the anti-commutation, or, to emphasize the grading, graded-commutative or, if the supercommutativity is understood, simply commutative.Any commutative algebra is a supercommutative algebra if given the trivial gradation (i.e. all elements are even). Grassmann algebras (also known as exterior algebras) are the most common examples of nontrivial supercommutative algebras. The supercenter of any superalgebra is the set of elements that supercommute with all elements, and is a supercommutative algebra.The even subalgebra of a supercommutative algebra is always a commutative algebra. That is, even elements always commute. Odd elements, on the other hand, always anticommute. That is,for odd x and y. In particular, the square of any odd element x vanishes whenever 2 is invertible:Thus a commutative superalgebra (with 2 invertible and nonzero degree one component) always contains nilpotent elements.".
- Supercommutative_algebra wikiPageID "859686".
- Supercommutative_algebra wikiPageRevisionID "543817992".
- Supercommutative_algebra hasPhotoCollection Supercommutative_algebra.
- Supercommutative_algebra subject Category:Algebras.
- Supercommutative_algebra subject Category:Super_linear_algebra.
- Supercommutative_algebra type Abstraction100002137.
- Supercommutative_algebra type Algebra106012726.
- Supercommutative_algebra type Algebras.
- Supercommutative_algebra type Cognition100023271.
- Supercommutative_algebra type Content105809192.
- Supercommutative_algebra type Discipline105996646.
- Supercommutative_algebra type KnowledgeDomain105999266.
- Supercommutative_algebra type Mathematics106000644.
- Supercommutative_algebra type PsychologicalFeature100023100.
- Supercommutative_algebra type PureMathematics106003682.
- Supercommutative_algebra type Science105999797.
- Supercommutative_algebra comment "In mathematics, a supercommutative algebra is a superalgebra (i.e. a Z2-graded algebra) such that for any two homogeneous elements x, y we haveEquivalently, it is a superalgebra where the supercommutatoralways vanishes.".
- Supercommutative_algebra label "Algebra supercommutativa".
- Supercommutative_algebra label "Supercommutative algebra".
- Supercommutative_algebra sameAs Algebra_supercommutativa.
- Supercommutative_algebra sameAs m.03j0db.
- Supercommutative_algebra sameAs Q3611545.
- Supercommutative_algebra sameAs Q3611545.
- Supercommutative_algebra sameAs Supercommutative_algebra.
- Supercommutative_algebra wasDerivedFrom Supercommutative_algebra?oldid=543817992.
- Supercommutative_algebra isPrimaryTopicOf Supercommutative_algebra.