Search results for "Commutative property"

showing 10 items of 34 documents

Una generalizzazione del birapporto sopra un anello

1990

We generalize to the case of the projective line over a (not necessarily commutative) ring the well-know theorem on the bijective maps preserving a given cross-ratio.

Discrete mathematicsRing (mathematics)Pure mathematicsGeneral MathematicsProjective lineBijectionAlgebra over a fieldCommutative propertyMathematicsRendiconti del Circolo Matematico di Palermo
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Varieties of superalgebras of almost polynomial growth

2011

Abstract Let V gr be a variety of superalgebras and let c n gr ( V gr ) , n = 1 , 2 , …  , be its sequence of graded codimensions. Such a sequence is polynomially bounded if and only if V gr does not contain a list of five superalgebras consisting of a commutative superalgebra, the infinite dimensional Grassmann algebra and the algebra of 2 × 2 upper triangular matrices with trivial and natural Z 2 -gradings. In this paper we completely classify all subvarieties of the varieties generated by these five superalgebras, by giving a complete list of finite dimensional generating superalgebras.

Discrete mathematicsSequencePolynomialPure mathematicsAlgebra and Number TheoryMathematics::Rings and AlgebrasTriangular matrixGrowthPolynomial identitySuperalgebrasuperalgebra growthBounded functionMathematics::Quantum AlgebraVarietyVariety (universal algebra)Mathematics::Representation TheoryExterior algebraCommutative propertyMathematicsJournal of Algebra
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Conjunction and Disjunction Among Conditional Events

2017

We generalize, in the setting of coherence, the notions of conjunction and disjunction of two conditional events to the case of n conditional events. Given a prevision assessment on the conjunction of two conditional events, we study the set of coherent extensions for the probabilities of the two conditional events. Then, we introduce by a progressive procedure the notions of conjunction and disjunction for n conditional events. Moreover, by defining the negation of conjunction and of disjunction, we show that De Morgan’s Laws still hold. We also show that the associative and commutative properties are satisfied. Finally, we examine in detail the conjunction for a family \(\mathcal F\) of t…

Discrete mathematicsSettore MAT/06 - Probabilita' E Statistica MatematicaComputer scienceConditional events · Conditional random quantities · Con- junction · Disjunction · Negation · Quasi conjunction · Coherent previ- sion assessments · Coherent extensions · De Morgan’s Laws02 engineering and technologyCoherence (philosophical gambling strategy)Settore MAT/01 - Logica Matematica01 natural sciencesDe Morgan's lawsConjunction (grammar)Set (abstract data type)010104 statistics & probabilitysymbols.namesakeNegation0202 electrical engineering electronic engineering information engineeringsymbols020201 artificial intelligence & image processing0101 mathematicsAlgorithmCommutative propertyAssociative propertyEvent (probability theory)
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Generalized Logical Operations among Conditional Events

2018

We generalize, by a progressive procedure, the notions of conjunction and disjunction of two conditional events to the case of n conditional events. In our coherence-based approach, conjunctions and disjunctions are suitable conditional random quantities. We define the notion of negation, by verifying De Morgan’s Laws. We also show that conjunction and disjunction satisfy the associative and commutative properties, and a monotonicity property. Then, we give some results on coherence of prevision assessments for some families of compounded conditionals; in particular we examine the Frechet-Hoeffding bounds. Moreover, we study the reverse probabilistic inference from the conjunction $\mathcal…

FOS: Computer and information sciencesSettore MAT/06 - Probabilita' E Statistica MatematicaComputer Science - Artificial IntelligenceComputer scienceMonotonic functionProbabilistic reasoning02 engineering and technologyCommutative Algebra (math.AC)Conditional random quantitieFréchet-Hoeffding boundCoherent extensionNegationArtificial IntelligenceQuasi conjunction0202 electrical engineering electronic engineering information engineeringFOS: MathematicsCoherent prevision assessmentConditional eventNon-monotonic logicRule of inferenceCommutative propertyAssociative propertyDiscrete mathematicsProbability (math.PR)Probabilistic logicOrder (ring theory)ConjunctionMathematics - LogicCoherence (philosophical gambling strategy)p-entailmentProbabilistic inferenceMathematics - Commutative AlgebraConjunction (grammar)Artificial Intelligence (cs.AI)020201 artificial intelligence & image processingInference ruleNegationLogic (math.LO)Mathematics - ProbabilityDisjunction
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Non-commutative geometry and covariance: From the quantum plane to quantum tensors

1994

Reflection and braid equations for rank two $q$-tensors are derived from the covariance properties of quantum vectors by using the $R$-matrix formalism.

High Energy Physics - TheoryPhysicsFormalism (philosophy of mathematics)High Energy Physics - Theory (hep-th)BraidFOS: Physical sciencesGeneral Physics and AstronomyCovarianceCommutative propertyQuantumMathematical physicsCzechoslovak Journal of Physics
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Supersymmetry in non commutative superspaces

2003

Non commutative superspaces can be introduced as the Moyal-Weyl quantization of a Poisson bracket for classical superfields. Different deformations are studied corresponding to constant background fields in string theory. Supersymmetric and non supersymmetric deformations can be defined, depending on the differential operators used to define the Poisson bracket. Some examples of deformed, 4 dimensional lagrangians are given. For extended superspace (N>1), some new deformations can be defined, with no analogue in the N=1 case.

High Energy Physics - TheoryPhysicsNuclear and High Energy PhysicsFOS: Physical sciencesFísicaSupersymmetrySuperspaceString theoryDifferential operatorNoncommutative geometryPoisson bracketQuantization (physics)High Energy Physics::TheoryNonlinear Sciences::Exactly Solvable and Integrable SystemsHigh Energy Physics - Theory (hep-th)Commutative propertyComputer Science::DatabasesParticle Physics - TheoryMathematical physics
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Differential algebras in non-commutative geometry

1993

We discuss the differential algebras used in Connes' approach to Yang-Mills theories with spontaneous symmetry breaking. These differential algebras generated by algebras of the form functions $\otimes$ matrix are shown to be skew tensorproducts of differential forms with a specific matrix algebra. For that we derive a general formula for differential algebras based on tensor products of algebras. The result is used to characterize differential algebras which appear in models with one symmetry breaking scale.

High Energy Physics - TheoryPhysicsPure mathematicsDifferential formSpontaneous symmetry breakingFOS: Physical sciencesGeneral Physics and AstronomyOf the formMatrix (mathematics)Tensor productHigh Energy Physics - Theory (hep-th)Mathematics - Quantum AlgebraFOS: MathematicsQuantum Algebra (math.QA)Differential algebraGeometry and TopologySymmetry breakingCommutative propertyMathematical PhysicsJournal of Geometry and Physics
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Gravity, Non-Commutative Geometry and the Wodzicki Residue

1993

We derive an action for gravity in the framework of non-commutative geometry by using the Wodzicki residue. We prove that for a Dirac operator $D$ on an $n$ dimensional compact Riemannian manifold with $n\geq 4$, $n$ even, the Wodzicki residue Res$(D^{-n+2})$ is the integral of the second coefficient of the heat kernel expansion of $D^{2}$. We use this result to derive a gravity action for commutative geometry which is the usual Einstein Hilbert action and we also apply our results to a non-commutative extension which, is given by the tensor product of the algebra of smooth functions on a manifold and a finite dimensional matrix algebra. In this case we obtain gravity with a cosmological co…

High Energy Physics - TheoryPhysicsResidue (complex analysis)General Physics and AstronomyFOS: Physical sciencesGeometryCosmological constantGeneral Relativity and Quantum Cosmology (gr-qc)Riemannian manifoldDirac operatorGeneral Relativity and Quantum Cosmologysymbols.namesakeGeneral Relativity and Quantum CosmologyTensor productHigh Energy Physics - Theory (hep-th)Einstein–Hilbert actionsymbolsGeometry and TopologyCommutative propertyMathematical PhysicsHeat kernel
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Lattices of Jordan algebras

2010

AbstractCommutative Jordan algebras play a central part in orthogonal models. The generations of these algebras is studied and applied in deriving lattices of such algebras. These lattices constitute the natural framework for deriving new orthogonal models through factor aggregation and disaggregation.

Kronecker productNumerical AnalysisPure mathematicsProjectorsAlgebra and Number TheoryJordan algebraNon-associative algebraBinary operationsLatticeAlgebrasymbols.namesakeBinary operationCommutative Jordan algebraLattice (order)Kronecker matrix productsymbolsDiscrete Mathematics and CombinatoricsGeometry and TopologyNest algebraCommutative algebraCommutative propertyMathematicsLinear Algebra and its Applications
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Star-free trace languages

1992

Abstract Generalizing a classical result of Schutzenberger to free partially commutative monoids, we prove that the family of star-free trace languages coincides with the family of aperiodic trace languages.

MonoidPure mathematicsGeneral Computer ScienceAbstract family of languagesComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Star (graph theory)Cone (formal languages)Theoretical Computer ScienceTrace (semiology)Aperiodic graphFormal languageComputer Science::Programming LanguagesCommutative propertyMathematicsComputer Science(all)Theoretical Computer Science
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