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{{Short description|Ordered field with a function generalizing the exponential function}} ...with a function which generalises the idea of exponential functions on the ordered field of real numbers. ...

{{Short description|Ordered field that does not satisfy the Archimedean property}} In mathematics, a '''non-Archimedean ordered field''' is an [[ordered field]] that does not satisfy the [[Archimedean property]]. Such fields wi ...

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

...d]]s, varieties of finite [[ordered semigroup]]s and varieties of finite [[ordered monoid]]s are defined similarly. === Algebraic definition === ...

In [[abstract algebra]], a '''partially ordered ring''' is a [[Ring (mathematics)|ring]] (''A'', +, '''·'''), together with ...G. |date=December 1960 | title = A structure theory for a class of lattice-ordered rings | journal = Acta Mathematica | volume = 104 | issue = 3–4 | pag ...

...sses that <math>a \leq c</math></ref> <math>M</math> is called ''naturally ordered'' if the <math>\leq</math> relation is additionally [[antisymmetric relatio ...not a partial order. There are also examples of monoids that are naturally ordered but are not semirings with monus.<ref>{{cite web ...

...s closed under [[continuous function|continuous]] [[Semialgebraic set|semi-algebraic]] functions defined over the [[integer]]s. ...all continuous [[semialgebraic set|semi-algebraic function]]s on a [[semi-algebraic set]] of a real closed field (with values in that field). Also, the subring ...

...rmation]]. Often, this revolves around using [[Category theory|categorical structures]] or [[Cohomology|cohomology theories]] to classify and describe various to ...e objects the categories describe some sort of [[quasiparticles]], and the structures on the category encode the ways in which these quasiparticles can interact ...

...of 1993 International Conference on Computer Aided Design (ICCAD) |chapter=Algebraic decision diagrams and their applications |chapter-url=https://doi.org/10.11 ...<math>\{0,1\}^n</math> to a finite set of constants S, or carrier of the [[algebraic structure]]. An ADD is a rooted, directed, acyclic graph, which has several ...

...ematical logic)|structure]] (''M'',&lt;,...) that is [[Total order|totally ordered]] by < is called an '''o-minimal structure''' if and only if every [[defina ...ers in ''M''. This is analogous to the [[strongly minimal theory|minimal]] structures, which are exactly the analogous property down to equality. ...

'''Algebraic statistics''' is the use of [[algebra]] to advance [[statistics]]. Algebra ...has been sometimes restricted, sometimes being used to label the use of [[algebraic geometry]] and [[commutative algebra]] in statistics. ...

...concept of a '''residuated mapping''' arises in the theory of [[partially ordered set]]s. It refines the concept of a [[monotonic function|monotone function If ''A'', ''B'' are [[Partially ordered sets|posets]], a function ''f'': ''A'' → ''B'' is defined to be monotone if ...

...0" /> and can also be generalized to other [[Algebraic structure|algebraic structures]] such as [[Ring (mathematics)|rings]].<ref name=":1" /> * The set of commuting probabilities of finite groups is reverse-well-ordered, and the reverse of its order type is known to be either <math>\omega^\omeg ...

...aps were first introduced by [[Richard P. Stanley]] while studying ordered structures and partitions as a Ph.D. student at [[Harvard University]] in 1971 under t Let <math>P</math> be a [[Finite set|finite]] [[partially ordered set|poset]] with <math>p</math> elements denoted <math>x,y \in P</math>, an ...

{{Short description|Element of algebraic structure}} In [[mathematics]], a '''Garside element''' is an element of an [[algebraic structure]] such as a [[monoid]] that has several desirable properties. ...

A field is an algebraic structure composed of a set of elements, ''F'', two [[binary operation]]s, ...dering the [[ordered field]] '''R''' equipped with this function gives the ordered real exponential field, denoted {{nowrap|1='''R'''_exp = ('''R''' ...

...f topological spaces|seven definitions]]; [[ordered field]] has at least [[Ordered field#Definition|two definitions]]). ==Deduced structures and cryptomorphisms== ...

...th>u\in\mathrm{F}_{p}(M)\,</math> at point <math>p\in M\, ,</math> i.e. an ordered basis <math>({\mathbf e}_1,\dots,{\mathbf e}_n,{\mathbf f}_1,\dots,{\mathbf [[Category:Structures on manifolds]] ...

...ebraic properties of events that can be observed in [[quantum mechanics]]. Structures equivalent to effect algebras were introduced by three different research g ...first1=Anatolij|last2=Pulmannová|first2=Sylvia|title=New Trends in Quantum Structures|year=2000|section=1.3|publisher=Kluwer Academic Publishers, Dordrecht|isbn= ...

...rrections|location=Providence, Rhode Island|oclc=882503487}}</ref> is an [[algebraic structure]] consisting of a [[set (mathematics)|set]] together with a [[bin The [[direct product]] <math>R_{gz} = G \times Z</math> of these two structures is defined as follows: ...