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...izes a [[group scheme]], which is a scheme whose sets of points have group structures in a compatible way. ...scheme is a group-stack. More generally, a '''group algebraic-space''', an algebraic-space analog of a group scheme, is a group-stack. ...

In mathematics, '''BF algebras''' are a class of algebraic structures arising out of a symmetric "Yin Yang" concept for Bipolar Fuzzy logic, the [[Category:Algebraic structures]] ...

...ebraic-characterizations-of-inverse-semigroups-and-strongly-regular-rings/ Algebraic characterizations of inverse semigroups and strongly regular rings] theorem [[Category:Algebraic structures]] ...

In [[algebraic topology]], several types of products are defined on homological and cohomo *[[Differential graded algebra]]: the algebraic structure arising on the cochain level for the cup product ...

{{Group-like structures}} ...allo |editor3=Jim Stasheff|title=Associahedra, Tamari Lattices and Related Structures: Tamari Memorial Festschrift|url=https://archive.org/details/associahedrata ...

...ndation for the definition of [[invertible sheaf|invertible sheaves]] in [[algebraic geometry]]. ...n]] one [[algebraic variety|varieties]] including the theory of [[divisor (algebraic geometry)|divisor]]s. ...

...o <math>\mathbb{R}^{2n}</math> for some ''n'', but is not isomorphic as an algebraic variety to <math>\mathbb{C}^n</math>.<ref>{{citation ...: Proceedings of the Conference Interesting Algebraic Varieties Arising in Algebraic Transformation Group Theory Held at the Erwin Schrödinger Institute, Vienna ...

...quirements between the comultiplication <math>\Delta</math> and the monoid structures on <math>H</math> and <math>H\otimes H</math>. ...

...gorithm is therefore fundamental, and it is widely used in [[computational algebraic geometry]]. ==Failure with algebraic sets== ...

...eometry|geometric object]], for example a [[Point_(geometry)|point]], an [[algebraic variety]], a [[vector bundle]], or a [[Sheaf (mathematics)|sheaf]], has som ...Since the work of Mumford, stability has appeared in many forms throughout algebraic geometry, often with various notions of stability either derived from geome ...

In [[algebraic geometry]], a '''log structure''' provides an abstract context to study [[s ...</math>).<ref name="Ogus">[[Arthur Ogus]] (2011). Lectures on Logarithmic Algebraic Geometry.</ref> ...

...y are also of purely mathematical interest in [[differential geometry]], [[algebraic topology]], and [[K theory]]. They form the foundation for symplectic spin Two metaplectic structures <math>({\mathbf P_1},F_{\mathbf P_1})</math> and <math>({\mathbf P_2},F_{\m ...

== Algebraic structures == ...

== Algebraic expressions == [[File:Exp-tree-ex-12.svg|thumb|270px|right|Binary algebraic expression tree equivalent to ((5 + z) / -8) * (4 ^ 2)]] ...

In [[algebraic geometry]], a '''level structure''' on a [[space (mathematics)|space]] ''X' ...rming a [[quotient (algebraic geometry)|quotient]]; thus introducing level structures helps overcome this difficulty. ...

...chapter=Constraints and Application Conditions: From Graphs to High-Level Structures | editor1=Ehrig H. |editor2=Engels G. |editor3=Parisi-Presicce F. |editor4= ...sited", Habel, Annegret and Müller, Jürgen and Plump, Detlef, Mathematical Structures in Computer Science, vol. 11, no. 05., pp. 637--688, 2001, Cambridge Univer ...

[[Category:Free algebraic structures]] ...

...roperties. Those classes can be defined in two distinct ways, using either algebraic notions or topological notions. Varieties of finite [[monoid]]s, varieties === Algebraic definition === ...

...349|doi=10.1007/bfb0066716}}</ref> and the construction of the [[Moduli of algebraic curves|moduli stack of pointed curves]].<ref>{{Cite journal|last=Knudsen|fi ...)</math></blockquote>An element of <math>x \in F(X)</math> is called an '''algebraic element''' if it is the henselization of an <math>\mathcal{O}_S</math>-alge ...

...cite book | last=Hatcher | first=Allen | author-link=Allen Hatcher | title=Algebraic Topology | publisher=[[Cambridge University Press]] | year=2002 | isbn=0-52 ...s map between spaces is associated with a structure-preserving map between structures, called an induced homomorphism. ...