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{{short description|Theorem in algebra}} ...ter ''Z'', the ring <math>A \otimes_Z Z_{(0)}</math> is a [[central simple algebra]] over <math>Z_{(0)}</math>, the [[field of fractions]] of ''Z''.<ref>{{har ...

...quality''' is an inequality involving extensions of [[valued field]]s in [[algebra]], introduced by {{harvs|txt|authorlink=Shreeram Shankar Abhyankar|last=Abh ...ion | last1=Abhyankar | first1=Shreeram | title=On the valuations centered in a local domain | jstor=2372519 | mr=0082477 | year=1956 | journal=[[Americ ...

{{Short description|Theorem in algebra}} ...ow.net/questions/159735/in-what-generality-does-eilenberg-watts-hold|title=In what generality does Eilenberg-Watts hold?|website=MathOverflow}}</ref> ...

{{short description|Formula relating pairs of elements in a division ring}} {{for|Hua's identity in [[Jordan algebra]]s|Hua's identity (Jordan algebra)}} ...

...nd the relations).<ref>{{harvnb|Procesi|2007|loc=Ch. 9, § 1.4.}}</ref> The theorems are among the most important results of [[invariant theory]]. ...haracteristic (algebra)|characteristic]]-free invariant theory extends the theorems to a [[field (mathematics)|field]] of arbitrary characteristic.<ref>{{harvn ...

...[functional analysis]]. It states that in a [[unital algebra|unital]] [[C*-algebra]], the closure of the [[convex hull]] of the [[unitary element]]s is the cl ...A. Belfi | title = Characterizations of C*-Algebras: The Gelfand–Naimark Theorems | publisher = Marcel Dekker | location = New York | year = 1986 | isbn = 0- ...

...rnal|last1=Krull|first1=Wolfgang|title=Zur Theorie der zweiseitigen Ideale in nichtkommutativen Bereichen|journal=Mathematische Zeitschrift|volume=28|iss ...iplicative system (''i.e.'' <math>M</math> is closed under multiplication) in a [[Ring (mathematics)|ring]] <math>R</math>, and suppose ...

...ommutative Algebra with a View Toward Algebraic Geometry'', Graduate Texts in Mathematics, 150, Springer-Verlag, 1995, {{ISBN|0-387-94268-8}}, Exercise 4 ...nd <math>B \sub C</math> [[commutative algebra (structure)|commutative]] [[algebra over a ring|algebras over ''A'']]. If ''C'' is of finite type over ''A'' an ...

In [[abstract algebra]], an '''[[automorphism]] of a [[Lie algebra]]''' <math>\mathfrak g</math> is an [[isomorphism]] from <math>\mathfrak g< ...operatorname{Aut}^0(\mathfrak{g})</math>. These form a [[normal subgroup]] in the group of automorphisms, and the [[quotient group|quotient]] <math>\oper ...

In [[commutative algebra]], the '''Auslander–Buchsbaum formula''', introduced by {{harvs|txt|last=Au ...local ring|regular]] if, and only if, it has finite [[global dimension]]. In turn this implies that the [[localization of a ring|localization]] of a reg ...

{{short description|Example of a non-commutative and non-cocommutative Hopf algebra}} ...xample of an infinite-dimensional [[Hopf algebra]], and '''Sweedler's Hopf algebra''' ''H''₄ is a certain 4-dimensional quotient of it that is nei ...

{{DISPLAYTITLE:Basic theorems in algebraic ''K''-theory}} {{short description|Four mathematical theorems}} ...

In [[mathematics]], the '''B-theorem''' is a result in [[Group theory#Finite group theory|finite group theory]] formerly known as [[Category:Theorems about finite groups]] ...

{{Short description|Theorem of operator algebra}} ...n algebras]] and so-called domains of positivity. Thus it links [[operator algebra]]ic and [[Convex function|convex]] [[Order theory|order theoretic]] views o ...

In mathematics, specifically in the study of [[vector bundle]]s over [[Kähler manifold|complex Kähler manif ...first2=Shigeo|date=1954|title=Note on Kodaira-Spencer's proof of Lefschetz theorems|url=https://projecteuclid.org/euclid.pja/1195526105|journal=Proceedings of ...

In [[algebraic geometry]], the '''Atiyah–Bott formula''' says<ref>{{harvnb|Gai ...] is a [[free algebra|free]] [[supercommutative algebra|graded-commutative algebra]] on certain homogeneous generators. The original work of [[Michael Atiyah] ...

In [[linear algebra]], let {{math|1=''A''&nbsp;=&nbsp;(''a_ij'')}} be a {{math|''n'' ...55-1 |edition=2nd |page=92 |chapter=Basic Iterative Methods and Comparison Theorems}}</ref> ...

In [[mathematics]], at the intersection of [[algebraic topology]] and [[algebr == Structure theorems == ...

{{Short description|Concept in Algebra}}In [[algebra]], more specifically [[group theory]], a ''p''-'''elementary group''' is a ...tp://wwwmath.uni-muenster.de/u/bartelsa/research/induction.pdf ''Induction Theorems and Isomorphism Conjectures for K- and L-Theory''] ...

...iven theorem''' is a theorem that generalizes the [[fundamental theorem of algebra]] to quaternionic [[polynomial]]s, that is, polynomials with [[quaternion]] ...american-mathematical-society/volume-50/issue-4/The-fundamental-theorem-of-algebra-for-quaternions/bams/1183505735.full|journal=[[Bulletin of the American Mat ...