Search results

{{Short description|Abstract algebra polynominal in mathematics}} ...> over a field that can be expressed as a polynomial in the sum of squares of the variables. That is, if ...

{{Short description|Branch of mathematics}} ...aic topology|nonabelian algebraic topology]], and in particular the theory of [[closed model category|closed model categories]]. ...

...was a Russian [[mathematician]] known for his contributions to [[abstract algebra]]. ...was scientific secretary from the mid-1960s to the early 1970s) and taught algebra at the [[St. Petersburg University]]. He died on September 15, 2003, in St. ...

...rominent examples of commutative rings include [[polynomial ring]]s, rings of [[algebraic integer]]s, including the ordinary [[integer]]s <math>\mathbb{Z == Research fields == ...

...to a proof that relies on category-theoretic methods, or even to the study of category theory itself. ...ril 2001, Volume 33, nos. 2 and 3. Online version available at http://www.fields.utoronto.ca/aboutus/FieldsMedal_Monastyrsky.pdf. ...

...of the algebraization of deductive systems, based on the Lindenbaum–Tarski algebra}} ...logic]], '''abstract algebraic logic''' is the study of the algebraization of [[deductive system]]s ...

{{short description|Class of extensions of the real numbers}} ...]]s. The [[Field (mathematics)|field]] of superreals is itself a subfield of the [[surreal number]]s. ...

...''C'' is a [[central simple algebra]] over some [[field extension]] ''L'' of the field ''K'' over which the [[quadratic form]] ''Q'' defining ''C'' is d ...the signature {{nowrap|''p'' − ''q'' (mod 8)}}. This is an algebraic form of [[Bott periodicity]]. ...

part of the set of 830+ outlines listed at a special type of list article. ...

In [[abstract algebra]], a branch of [[mathematics]], a '''simple ring''' is a [[zero ring|non-zero]] [[ring (ma ...an [[associative algebra]] over this field. It is then called a '''simple algebra''' over this field. ...

{{wiktionary|Appendix:Glossary of abstract algebra}} ...eal numbers|real]] or [[complex number]]s, often now called ''[[elementary algebra]]''. The distinction is rarely made in more recent writings. ...

...e ring]]. Semiprimitive rings can be understood as [[subdirect product]]s of [[primitive ring]]s, which are described by the [[Jacobson density theorem] A ring is semiprimitive if and only if it is a subdirect product of left primitive rings. ...

...[[Group extension|extensions]] of an abelian group. Every finite extension of a [[finite field]] is a cyclic extension. ...an algebraic variety|function fields]] of [[algebraic curve]]s over finite fields, and [[local field]]s. ...

...ring extension]] whose properties are relatively well understood. Elements of a Ore extension are called '''Ore polynomials'''. ...veloping algebra]]s of [[solvable Lie algebra]]s, and [[coordinate ring]]s of [[quantum group]]s. ...

...This means that depending on the generators and relations, a universal C*-algebra may not exist. In particular, free C*-algebras do not exist. == C*-Algebra Relations == ...

{{Short description|Abstract algebra concept}} ...integer]]s and the field of [[rational number]]s. Intuitively, it consists of ratios between integral domain elements. ...

...h should not be confused with the similar-sounding but more general notion of [[radical extension]]s. ...nus F</math>, the [[Minimal polynomial (field theory)|minimal polynomial]] of <math>\alpha</math> over ''F'' is ''not'' a [[separable polynomial]].<ref n ...

* [[Axiom of extensionality]] * [[Extension (predicate logic)]], the set of tuples of values that satisfy the predicate ...

{{Short description|Concept in abstract algebra}} ...ative algebra over <math>K</math> is an [[extension field]] <math>L</math> of <math>K</math>. ...

...gebra]], a [[field (mathematics)|field]] ''k'' is '''perfect''' if any one of the following equivalent conditions holds: ...al]] over ''k'' has no [[Multiplicity (mathematics)#Multiplicity of a root of a polynomial|multiple roots]] in any [[field extension]] ''F/k''. ...