Search results

...quality''' is an inequality involving extensions of [[valued field]]s in [[algebra]], introduced by {{harvs|txt|authorlink=Shreeram Shankar Abhyankar|last=Abh ...us the rank of the [[quotient]] of the [[valuation group]]s; here the rank of an abelian group <math>A</math> is defined as <math>\dim_{\mathbb{Q}}(A \ot ...

...ws|title=On Structurable algebras|author=R.D. Schafer|journal=[[Journal of Algebra]]|year=1985|volume=92|pages=400–412}}</ref> ...E_7|author=Skip Garibaldi|author-link=Skip Garibaldi|journal=[[Journal of Algebra]]|volume=236|year=2001|pages=651–691}}</ref> ...

...l Features of the Real and Rational Numbers|volume=112|series=Encyclopedia of Mathematics and its Applications|first=H.|last=Salzmann|publisher=Cambridge ..., corresponding to two [[coset]]s: the set of positive numbers and the set of negative numbers. Thus, the real numbers have two square classes, the posit ...

{{Other uses of|graded|Grade (disambiguation){{!}}Grade}} In [[mathematics]], the term "'''graded'''" has a number of meanings, mostly related: ...

...xtension|simple]] if and only if there are only finitely many intermediate fields between <math>K</math> and <math>L</math>. ...math>) simply the degree of <math>g</math>. Therefore, by multiplicativity of degree, <math>[M:M'] = 1</math> and hence <math>M = M'</math>. ...

...an integral domain when <math>\overline{k}</math> is the algebraic closure of <math>k</math> (that is, to say, <math>L, \overline{k}</math> are [[linearl * The extension ''L''/''k'' is regular if and only if every subfield of ''L'' finitely generated over ''k'' is regular over ''k''.<ref name=C425/> ...

{{short description|Algebraic number fields are determined by their absolute Galois groups}} ...994}} extended the result to infinite fields that are [[Finitely generated algebra|finitely generated]] over [[prime field]]s. ...

...lgebra)|resolution]] of the module by [[flat module]]s. The weak dimension of a module is, at most, equal to its [[projective dimension]]. ...be infinite. It is at most equal to the left or right [[global dimension]] of the ring ''R''. ...

In [[abstract algebra | algebra]], a '''change of rings''' is an operation of changing a coefficient ring to another. ...ath>f: R \to S</math>, there are three ways to change the coefficient ring of a [[module (mathematics)|module]]; namely, for a right ''R''-module ''M'' a ...

{{Short description | Differential geometry of supermanifolds}} ...upermanifold]]s and [[graded manifold]]s. Supergeometry is part and parcel of many classical and quantum [[field theory (physics)|field theories]] involv ...

...tle=DG coalgebras as formal stacks|journal = [[Journal of Pure and Applied Algebra]] | volume= 162| year=2001|issue =2–3 | pages=209–250| mr= 1843805| doi=10. ...oplus L_i</math> over a [[field (mathematics)|field]] of [[characteristic (algebra)|characteristic]] zero together with a bilinear map <math>[\cdot,\cdot]\col ...

...of certain [[Motivic cohomology|motivic complex]]es coincides with pieces of [[Algebraic K-theory|K-groups]]. It extends a conjecture due to {{harvs|txt He conjectured that ''i''-th cohomology of this complex is isomorphic to the motivic cohomology group <math>H^i_{mot}( ...

{{Short description|Algebra over a field with only invertible elements and zero}} ...[[abstract algebra]], a '''division algebra''' is, roughly speaking, an [[algebra over a field]] in which [[division (mathematics)|division]], except by zero ...

{{Short description|Subset of a ring that forms a ring itself}} ...dentity]] as {{mvar|R}}.<ref group=lower-alpha>In general, not all subsets of a ring {{mvar|R}} are rings.</ref> ...

...ean metric <math>|x-y|</math>. Since it is constructed from the completion of <math>\Q</math> with respect to this metric, it is a complete field. Extend ...math>c,</math> its valuation is the integer <math>n</math>. The completion of <math>\Q</math> by <math>v_p</math> is the complete field <math>\Q_p</math> ...

...Hermite|eprint=1209.5371|year=2012|class=math.HO}} (See footnote at bottom of page 18.)</ref><ref>{{cite book|title=Catalogue général de la librairie fra ...is theorem in his paper ''Sur l'équation du sixième degré'' in ''tome'' 64 of [[Comptes rendus de l'Académie des Sciences|''Comptes rendus hebdomadaires ...

{{Short description|Generalization of the Dirac equation}} ...hysics]], '''the Dirac equation in curved spacetime''' is a generalization of the [[Dirac equation]] from flat spacetime ([[Minkowski space]]) to curved ...

...ne Schilling with Cristian Lenart at the [[Mathematical Research Institute of Oberwolfach|MFO]], 2011]] ...hematical physics]]. She is a professor of mathematics at the [[University of California, Davis]]. ...

...²), the area of the green region (=Y²), and the area of the two white regions (=2×X×Y).]] ...nited States]] as the [[FOIL method]]). For larger positive integer values of ''n'', the correct result is given by the [[binomial theorem]]. ...

...sburg]</ref> is a German mathematician, specializing in [[abstract algebra|algebra]], [[algebraic number theory]], and [[algebraic geometry]]. ...sity of Cologne]] and since 1999 he has been a professor at the University of Regensburg. ...