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...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> ...

...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 ...

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 ...

...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 mathematics, the '''Kuratowski–Ryll-Nardzewski measurable selection theorem ...st3=José |date=2010 |title=Measurability and Selections of Multi-Functions in Banach Spaces ...

{{Short description|Mathematical theorem in algebra}} {{Too abstract|date=April 2022}} ...

In abstract algebra, '''multiplicity theory''' concerns the '''multiplicity of a module''' ''M' ...e's intersection formula, it is linked to an [[intersection multiplicity]] in the [[intersection theory]]. ...

In [[mathematics]], '''Littlewood's Tauberian theorem''' is a strengthening of ...n ''a''_''n'' &ge; –''C''/''n'' for some constant ''C''. However in some sense the condition is optimal: Littlewood showed that if ''c''<sub>'' ...

In [[Field (mathematics)|field theory]], '''Steinitz's theorem''' states that ...s simple, that is to say <math>L = K(\alpha)</math> for some <math>\alpha \in L</math>. Let <math>M</math> be any intermediate field between <math>L</mat ...

...[[Hopf algebras]], of the sort that often show up as [[cohomology]] rings in [[algebraic topology]]. ...] zero with <math>\dim A_n < \infty</math> for all ''n'', the natural Hopf algebra homomorphism ...

In mathematics, the '''Andreotti–Grauert theorem''', introduced by {{harvs|txt ...nal |url=https://eudml.org/doc/183771 |title=Cohomology of q-convex Spaces in Top Degrees |journal=Mathematische Zeitschrift |date=1990 |volume=204 |issu ...

...a subring]] ''S'' of a ring ''R'', denoted '''C'''_''R''(''S'') in this article. It is always the case that '''C'''_''R''('''C'''<su :<math>\mathrm{C}_R(S)=\{r\in R \mid rs=sr \text{ for all } s\in S\}.\,</math> ...

...asayoshi Nagata}}, implies that every [[abstract variety]] can be embedded in a [[complete variety]], and more generally shows that a [[Glossary of schem ...used the older terminology of [[Zariski–Riemann space]]s and [[Valuation (algebra)|valuation theory]], which sometimes made it hard to follow. ...

...em]] <math>\Phi</math>, there exists a finite-dimensional [[semisimple Lie algebra]] whose root system is the given <math>\Phi</math>. ...<math>\{ \alpha_1, \dots, \alpha_n \}</math> of <math>\Phi</math>, the Lie algebra <math>\mathfrak g</math> defined by (1) <math>3n</math> generators <math>e_ ...

{{short description|On when a morphism of spectral sequences in homological algebra is an isomorphism}} In [[homological algebra]], '''Zeeman's comparison theorem''', introduced by [[Christopher Zeeman]], ...

{{Short description|Theorem in algebra}} ...[module (mathematics)|modules]] over a complete Noetherian [[local ring]]. In the special case when the local ring has a field{{clarify|reason=As a subfi ...

...29|bibcode=2014CRMat.352..773R |s2cid=1345373}}</ref> The theorem is named in honor of Charles Joubert, a French mathematician, ''[[lycée]]'' professor, ...ert published his theorem in his paper ''Sur l'équation du sixième degré'' in ''tome'' 64 of [[Comptes rendus de l'Académie des Sciences|''Comptes rendus ...

...&nbsp;1) is called '''semiprimary''' if ''R''/''J''(''R'') is [[semisimple algebra|semisimple]] and ''J''(''R'') is a [[nilpotent ideal]], where ''J''(''R'') ...0/17_0_337/_article}}</ref> for [[commutative ring]]s a few years earlier, in 1935. ...

...lity property for types called tameness. Even though it appears implicitly in earlier work of [[Saharon Shelah|Shelah]], tameness as a property of AEC wa ...' to ''b'' fixing <math>M</math> pointwise (note that types can be defined in a similar manner without using a monster model<ref>{{harvnb|Shelah|2009}}, ...