Editing Superalgebra (section)

==Examples==
*Any algebra over a commutative ring ''K'' may be regarded as a purely even superalgebra over ''K''; that is, by taking ''A''<sub>1</sub> to be trivial.
*Any '''Z'''- or '''N'''-[[graded algebra]] may be regarded as superalgebra by reading the grading modulo 2. This includes examples such as [[tensor algebra]]s and [[polynomial ring]]s over ''K''.
*In particular, any [[exterior algebra]] over ''K'' is a superalgebra. The exterior algebra is the standard example of a [[supercommutative algebra]].
*The [[symmetric polynomials]] and [[alternating polynomials]] together form a superalgebra, being the even and odd parts, respectively. Note that this is a different grading from the grading by degree.
*[[Clifford algebra]]s are superalgebras. They are generally noncommutative.
*The set of all [[endomorphism]]s (denoted <math>\mathbf{End} (V) \equiv \mathbf{Hom}(V,V)</math>, where the boldface <math>\mathrm {Hom}</math> is referred to as ''internal'' <math>\mathrm {Hom}</math>, composed of ''all'' linear maps) of a [[super vector space]] forms a superalgebra under composition.
*The set of all square [[supermatrices]] with entries in ''K'' forms a superalgebra denoted by ''M''<sub>''p''|''q''</sub>(''K''). This algebra may be identified with the algebra of endomorphisms of a free supermodule over ''K'' of rank ''p''|''q'' and is the internal Hom of above for this space.
*[[Lie superalgebra]]s are a graded analog of [[Lie algebra]]s. Lie superalgebras are nonunital and nonassociative; however, one may construct the analog of a [[universal enveloping algebra]] of a Lie superalgebra which is a unital, associative superalgebra.