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...etween [[jordan algebra#Formally real Jordan algebras|formally real Jordan algebras]] and so-called domains of positivity. Thus it links [[operator algebra]]ic ...that these properties precisely characterize the positive cones of Jordan algebras. ...

...A. Belfi | title = Characterizations of C*-Algebras: The Gelfand–Naimark Theorems | publisher = Marcel Dekker | location = New York | year = 1986 | isbn = 0- ...=B. |author2=H. A. Dye |year=1966|title=A Note on Unitary Operators in C*-Algebras |journal=Duke Mathematical Journal |volume=33 |pages=413–416 |doi=10.1215/S ...

|title = Factorization in group algebras [[Category:Banach algebras]] ...

...assification of Lie algebras.<ref>{{harvnb|Humphreys|1972}}</ref> The only algebras with non-trivial outer automorphism group are therefore <math>A_n (n \geq 2 == Theorems == ...

...heodore Gamelin|chapter=3.3 Theorem (Walsh-Lebesgue Theorem)|title=Uniform Algebras|year=1984|pages=36–37|publisher=American Mathematical Society|isbn=97808218 ...ion algebra]]s such as the theory of [[Dirichlet algebra]]s and logmodular algebras.<ref>{{cite book|author=Walsh, J. L.|editor=Rivlin, Theodore J.|editor-link ...

...996|loc=Theorem 7.2.6.}}</ref><ref name="9.4 and 9.5">{{harvnb|Hall|2015}} Theorems 9.4 and 9.5</ref> There is a closely related theorem classifying the [[Comp ...orem is one of the key pieces of [[representation theory of semisimple Lie algebras]]. ...

...=Zhang | first3=Yinhuo | title=Structure theorems of H₄-Azumaya algebras | doi=10.1016/j.jalgebra.2005.10.020 | mr=2264134 | year=2006 | journal=[[J *{{Citation | last1=Montgomery | first1=Susan | title=Hopf algebras and their actions on rings | url=https://books.google.com/books?id=U895Bpub ...

...s the case that one can say the two sets are equal. The double centralizer theorems give conditions under which one can conclude that equality occurs. ===Central simple algebras=== ...

...f]] of [[groupoid]]s whose object sheaf and arrow sheaf are represented by algebras. Because any such presheaf will have an associated site, we can consider [[ == Structure theorems == ...

...ink=John Coleman Moore|year=1965}} classifies an important class of [[Hopf algebras]], of the sort that often show up as [[cohomology]] rings in [[algebraic to ...ilnor| last2 = Moore | first2 = John C. | title = On the structure of Hopf algebras | journal = [[Annals of Mathematics]] | volume = 81 | issue = 2 | year = 19 ...

...1=Dlab | first1=Vlastimil | last2=Ringel | first2=Claus Michael | title=On algebras of finite representation type | url=https://books.google.com/books?id=_JrnA [[Category:Theorems in representation theory]] ...

...vitt algebra]]s and may be considered as algebraic analogues of [[graph C*-algebras]]. Leavitt path algebras were simultaneously introduced in 2005 by [[Gene Abrams]] and Gonzalo Arand ...

...ath> [[commutative algebra (structure)|commutative]] [[algebra over a ring|algebras over ''A'']]. If ''C'' is of finite type over ''A'' and if ''C'' is finite [[Category:Theorems about algebras]] ...

...pringer.com/10.1007/s00006-007-0026-y|journal=Advances in Applied Clifford Algebras|language=en|volume=17|issue=2|pages=245–258|doi=10.1007/s00006-007-0026-y|s [[Category:Theorems about polynomials]] ...

leads to a complete description of finite-dimensional [[division algebras]] over algebraic number fields in terms of their [[Hasse invariant of an al Using the theory of [[Brauer group]], one shows that two central simple algebras ''A'' and ''B'' over an algebraic number field ''K'' are isomorphic over '' ...

...ttps://books.google.com/books?id=foG0rKKKXboC|title=Integral Closure: Rees Algebras, Multiplicities, Algorithms|last=Vasconcelos|first=Wolmer|date=2006-03-30|p [[Category:Theorems in ring theory]] ...

...m]], which itself is a special case of various abstract Tauberian theorems about [[Banach algebra]]s. [[Category:Tauberian theorems]] ...

...first=Victor|last=Kac|authorlink=Victor Kac|title=Infinite dimensional Lie algebras|edition= 3rd |publisher= [[Cambridge University Press]] |year=1990|isbn=0-5 ...| first=James E. |authorlink=James E. Humphreys| title=Introduction to Lie Algebras and Representation Theory | publisher=[[Springer-Verlag]] | location=Berlin ...

...ension, Coxeter groups, Artin groups, combinatorial group theory, monomial algebras, arithmetic of algebraic groups ...from Bar-Ilan University in 2000; his dissertation, titled "Central Simple Algebras", was carried under the advisorship of [[Louis Rowen]]. ...

== Difference rings, difference fields and difference algebras == ...last=Levin|title=Difference algebra}} Theorem 2.6.4</ref> One of the basic theorems in difference algebra asserts that every ascending chain of perfect differe ...