Search results for "Number"

showing 10 items of 3939 documents

Group graded algebras and multiplicities bounded by a constant

2013

AbstractLet G be a finite group and A a G-graded algebra over a field of characteristic zero. When A is a PI-algebra, the graded codimensions of A are exponentially bounded and one can study the corresponding graded cocharacters via the representation theory of products of symmetric groups. Here we characterize in two different ways when the corresponding multiplicities are bounded by a constant.

Discrete mathematicsPure mathematicsFinite groupAlgebra and Number TheoryMathematics::Commutative AlgebraGroup (mathematics)Zero (complex analysis)Polynomial identities Graded algebras cocharactersRepresentation theorySettore MAT/02 - AlgebraSymmetric groupBounded functionAlgebra over a fieldConstant (mathematics)MathematicsJournal of Pure and Applied Algebra
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Upper and lower approximations of general aggregation operators based on fuzzy rough sets

2015

Our paper deals with constructions of upper and lower general aggregation operators which act on fuzzy sets. These constructions are based on fuzzy rough sets and provide two approximations (upper and lower) of the pointwise extension and the t-extension of an ordinary aggregation operator. Considering two lattices of corresponding general aggregation operators we describe two approximate systems with respect to a lattice of fuzzy equivalence relations.

Discrete mathematicsPure mathematicsFuzzy classificationFuzzy mathematicsFuzzy setFuzzy set operationsFuzzy numberRough setFuzzy subalgebraDefuzzificationMathematics2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)
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Maximal function estimates and self-improvement results for Poincaré inequalities

2018

Our main result is an estimate for a sharp maximal function, which implies a Keith–Zhong type self-improvement property of Poincaré inequalities related to differentiable structures on metric measure spaces. As an application, we give structure independent representation for Sobolev norms and universality results for Sobolev spaces. peerReviewed

Discrete mathematicsPure mathematicsGeneral Mathematics010102 general mathematicsAlgebraic geometryharmoninen analyysi01 natural sciencesUniversality (dynamical systems)Sobolev inequalitySobolev spacesymbols.namesakeNumber theoryinequalities0103 physical sciencesPoincaré conjecturesymbolsharmonic analysisMaximal function010307 mathematical physicsDifferentiable function0101 mathematicsfunktionaalianalyysiepäyhtälötMathematics
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Linear quotients of Artinian Weak Lefschetz algebras

2013

Abstract We study the Hilbert function and the graded Betti numbers for “generic” linear quotients of Artinian standard graded algebras, especially in the case of Weak Lefschetz algebras. Moreover, we investigate a particular property of Weak Lefschetz algebras, the Betti Weak Lefschetz Property, which makes possible to completely determine the graded Betti numbers of a generic linear quotient of such algebras.

Discrete mathematicsPure mathematicsHilbert series and Hilbert polynomialAlgebra and Number TheoryProperty (philosophy)Mathematics::Commutative AlgebraBetti numberBetti Weak Lefschetz PropertyMathematics::Rings and AlgebrasArtinian algebraLinear quotientWeak Lefschetz Propertysymbols.namesakeQuotientWeak Lefschetz; Artinian algebra; QuotientsymbolsWeak Lefschetz Property Artinian algebra Linear quotientLefschetz fixed-point theoremWeak LefschetzMathematics::Symplectic GeometryQuotientMathematics
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A Decomposition Theorem for the Fuzzy Henstock Integral

2012

We study the fuzzy Henstock and the fuzzy McShane integrals for fuzzy-number valued functions. The main purpose of this paper is to establish the following decomposition theorem: a fuzzy-number valued function is fuzzy Henstock integrable if and only if it can be represented as a sum of a fuzzy McShane integrable fuzzy-number valued function and of a fuzzy Henstock integrable fuzzy number valued function generated by a Henstock integrable function.

Discrete mathematicsPure mathematicsIntegrable systemMathematics::General MathematicsLogicMathematics::Classical Analysis and ODEsFunction (mathematics)Fuzzy logicComputingMethodologies_PATTERNRECOGNITIONArtificial IntelligenceIf and only ifSettore MAT/05 - Analisi MatematicaFuzzy Henstock integral fuzzy McShane integral Henstock-Kurzweil and McShane equiintegrabilityFuzzy numberLocally integrable functionComputingMethodologies_GENERALMathematicsDecomposition theorem
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Algebras with involution with linear codimension growth

2006

AbstractWe study the ∗-varieties of associative algebras with involution over a field of characteristic zero which are generated by a finite-dimensional algebra. In this setting we give a list of algebras classifying all such ∗-varieties whose sequence of ∗-codimensions is linearly bounded. Moreover, we exhibit a finite list of algebras to be excluded from the ∗-varieties with such property. As a consequence, we find all possible linearly bounded ∗-codimension sequences.

Discrete mathematicsPure mathematicsJordan algebraAlgebra and Number TheoryNon-associative algebraSubalgebraQuadratic algebra∗-CodimensionsSettore MAT/02 - AlgebraInterior algebra*-polynomial identity T*-ideal *-codimensions.∗-Polynomial identityT∗-idealDivision algebraAlgebra representationNest algebraMathematics
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On a normal form of symmetric maps of [0, 1]

1980

A class of continuous symmetric mappings of [0, 1] into itself is considered leaving invariant a measure absolutely continuous with respect to the Lebesgue measure.

Discrete mathematicsPure mathematicsLebesgue measureLebesgue's number lemmaStatistical and Nonlinear Physics58F20Absolute continuityLebesgue integrationLebesgue–Stieltjes integrationsymbols.namesakeNonlinear system28D05symbolsInvariant (mathematics)Borel measureMathematical PhysicsMathematicsCommunications in Mathematical Physics
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Identities of *-superalgebras and almost polynomial growth

2015

We study the growth of the codimensions of a *-superalgebra over a field of characteristic zero. We classify the ideals of identities of finite dimensional algebras whose corresponding codimensions are of almost polynomial growth. It turns out that these are the ideals of identities of two algebras with distinct involutions and gradings. Along the way, we also classify the finite dimensional simple *-superalgebras over an algebraically closed field of characteristic zero.

Discrete mathematicsPure mathematicsPolynomialAlgebra and Number TheoryMathematics::Commutative Algebraalmost polynomial growthgraded involution010102 general mathematicsZero (complex analysis)Field (mathematics)010103 numerical & computational mathematics01 natural sciencesMatrix polynomialSquare-free polynomialSimple (abstract algebra)polynomial identity0101 mathematicsAlgebraically closed fieldCharacteristic polynomialMathematics
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The Herzog-Vasconcelos conjecture for affine semigroup rings

1999

Let S be a simplicial affine semigroup such that its semigroup ring A = k[S] is Buchsbaum. We prove for such A the Herzog-Vasconcelos conjecture: If the A-module Der(k)A of k-linear derivations of A has finite projective dimension then it is free and hence A is a polynomial ring by the well known graded case of the Zariski-Lipman conjecture.

Discrete mathematicsPure mathematicsRing (mathematics)Algebra and Number TheoryConjectureMathematics::Commutative AlgebraSemigroupPolynomial ringDimension (graph theory)Affine transformationMathematicsMathematicsIndraStra Global
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Associative rings with metabelian adjoint group

2004

Abstract The set of all elements of an associative ring R, not necessarily with a unit element, forms a monoid under the circle operation r∘s=r+s+rs on R whose group of all invertible elements is called the adjoint group of R and denoted by R°. The ring R is radical if R=R°. It is proved that a radical ring R is Lie metabelian if and only if its adjoint group R° is metabelian. This yields a positive answer to a question raised by S. Jennings and repeated later by A. Krasil'nikov. Furthermore, for a ring R with unity whose multiplicative group R ∗ is metabelian, it is shown that R is Lie metabelian, provided that R is generated by R ∗ and R modulo its Jacobson radical is commutative and arti…

Discrete mathematicsPure mathematicsRing (mathematics)Algebra and Number TheoryGroup (mathematics)Metabelian groupMultiplicative groupLocal ringRadical ringJacobson radicalMetabelian groupAssociative ringLie metabelian ringAdjoint grouplaw.inventionInvertible matrixlawUnit (ring theory)MathematicsJournal of Algebra
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