Unital
Unital In mathematics, an associative algebra is unital (some authors use unitary) if it contains ... algebras, polynomial algebras and matrix algebras, are unital, if rings are assumed to be so ... of functions considered in analysis are not unital, for instance the algebra of square integrable ... on some (non-compact) space. Given two unital algebras A and B, an algebra ...
http://en.wikipedia.org/wiki/Unital - 3k - Cached - Similar pages

Banach algebra
... is continuous. A Banach algebra is called "unital" if it has an identity element for ... complex n-by-n matrices becomes a unital Banach algebra if we equip it with ... multiplication and the supremum norm) is a unital Banach algebra. The algebra of all bounded ... is a Banach algebra. The algebra is unital if and only if the original space ... the operator norm as norm) is a unital Banach algebra. The set of all ...
http://en.wikipedia.org/wiki/Banach_algebra - 8k - Cached - Similar pages

User talk:Melchoir/Archive1
... The article provides a perfect example: a unital magma is not an algebraic structure, because ... is not an identity (and for general unital magmas, the identity element need not be ... However, for a certain substructure of a unital magmas, namely groups, the other properties guarantee ... the identity element, thus allowing these particular unital magmas to be recast as algebraic structures ... I see what you're saying about unital magmas. Of course, we could just ...
http://en.wikipedia.org/wiki/User_talk:Melchoir/Archive1 - 91k - Cached - Similar pages

Talk:Ring (mathematics)
... at the beginning of the article? "Non-unital ring" is somewhat deceptive, because non-unital is not required, "non-unital" just means "admitting the possibility unity doesn ... around a flurry of articles on non-unital ring theory (quite possible, it's a ... or they have to always say, "non-unital ring" 500,000 times, instead of ...
http://en.wikipedia.org/wiki/Talk:Ring_(mathematics) - 31k - Cached - Similar pages

Universal enveloping algebra
... more familiar, and possibly easier to handle) unital associative algebra which captures the important properties ... over K we find the "most general" unital associative K-algebra A such that the ... any Lie algebra over K. Given a unital associative K-algebra U and a Lie ... satisfies the following universal property: for any unital associative K-algebra A and Lie algebra ... → A L there exists a unique unital algebra homomorphism g: U → A ...
http://en.wikipedia.org/wiki/Universal_enveloping_algebra - 12k - Cached - Similar pages

Coalgebra
... in a certain sense dual to the unital associative algebras. One formulates the axioms of unital associative algebras in terms of commutative diagrams ... X]. Now K[X] is both a unital associative algebra and a coalgebra, and the ... bialgebras). If A is a finite-dimensional unital associative K-algebra, then its K-dual ... above, if A is a finite-dimensional unital associative K-algebra, then A * is ...
http://en.wikipedia.org/wiki/Coalgebra - 15k - Cached - Similar pages

Exterior algebra
... over a field K is a certain unital associative algebra which contains V as a ... 3), so that the algebra is unital associative. Universal property and construction Let V ... that Λ(V) is the "most general" unital associative K-algebra containing V with an ... by the following universal property: Given any unital associative K-algebra A and any K ... in V, then there exists precisely one unital algebra homomorphism f : Λ(V) → ...
http://en.wikipedia.org/wiki/Exterior_algebra - 26k - Cached - Similar pages

Adjoint functors
... answer regarding the way to get a (unital) ring from one that is not unital is simple enough (see examples below); this ... modules are left adjoints. Making a ring unital This example was discussed in section 1.3 above. Given a non-unital ring R, a multiplicative identity element can ... taking a ring to the underlying non-unital ring. Ring extensions. Suppose R and ...
http://en.wikipedia.org/wiki/Adjoint_functors - 43k - Cached - Similar pages

Associative algebra
... an associative algebra with one or a unital (or unitary) associative algebra. Such an algebra ... x, M(y,z)) Similarly, a unital associative algebra can be defined in terms ... an associative multiplication. In this case, a unital R-algebra A can equivalently be defined ... co-associative, and, if the algebra is unital, then the co-algebra must be unital as well. Note that bialgebras leave ...
http://en.wikipedia.org/wiki/Associative_algebra - 17k - Cached - Similar pages

User:Lethe/list of categories
... schemes K-Alg or Alg K associative unital algebras over field K homomorphisms y y ... y n n y comUnC*Alg commutative unital C* algebras *-homomorphisms y CRng commutative rings ... between them (not concrete) comUnC*Alg commutative unital C*-algebras with unital *-homomorphisms compTopGrp compact topological groups fdVect K ...
http://en.wikipedia.org/wiki/User:Lethe/list_of_categories - 28k - Cached - Similar pages