Search results for "rings"

showing 10 items of 434 documents

Dyck paths with a first return decomposition constrained by height

2018

International audience; We study the enumeration of Dyck paths having a first return decomposition with special properties based on a height constraint. We exhibit new restricted sets of Dyck paths counted by the Motzkin numbers, and we give a constructive bijection between these objects and Motzkin paths. As a byproduct, we provide a generating function for the number of Motzkin paths of height k with a flat (resp. with no flats) at the maximal height. (C) 2018 Elsevier B.V. All rights reserved.KeywordsKeyWords Plus:STATISTICS; STRINGS

Discrete mathematicsMathematics::CombinatoricsFirst return decompositionDyck and Motzkin pathsEnumerationHeightStatisticsGenerating function0102 computer and information sciences01 natural sciencesConstructiveTheoretical Computer ScienceConstraint (information theory)Combinatorics010104 statistics & probability010201 computation theory & mathematicsEnumerationBijectionDecomposition (computer science)Discrete Mathematics and CombinatoricsStrings0101 mathematics[MATH]Mathematics [math]MathematicsPeak
researchProduct

A-Codes from Rational Functions over Galois Rings

2006

In this paper, we describe authentication codes via (generalized) Gray images of suitable codes over Galois rings. Exponential sums over these rings help determine--or bound--the parameters of such codes.

Discrete mathematicsMathematics::Commutative AlgebraApplied MathematicsFundamental theorem of Galois theoryGalois groupRational functionExponential polynomialComputer Science ApplicationsEmbedding problemDifferential Galois theorysymbols.namesakeGalois rings Gray map codesComputer Science::Computer Vision and Pattern RecognitionComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONComputer Science::MultimediasymbolsSettore MAT/03 - GeometriaGalois extensionResolventMathematicsDesigns, Codes and Cryptography
researchProduct

THE STRUCTURE OF MUTUALLY PERMUTABLE PRODUCTS OF FINITE NILPOTENT GROUPS

2007

We consider mutually permutable products G = AB of two nilpotent groups. The structure of the Sylow p-subgroups of its nilpotent residual is described.

Discrete mathematicsMathematics::Group TheoryPure mathematicsNilpotentGeneral MathematicsMathematics::Rings and AlgebrasSylow theoremsStructure (category theory)Permutable primeNilpotent groupMathematics::Representation TheoryMathematicsInternational Journal of Algebra and Computation
researchProduct

Polynomial identities on superalgebras: Classifying linear growth

2006

Abstract We classify, up to PI-equivalence, the superalgebras over a field of characteristic zero whose sequence of codimensions is linearly bounded. As a consequence we determine the linear functions describing the graded codimensions of a superalgebra.

Discrete mathematicsPolynomialPure mathematicsSequenceAlgebra and Number TheoryMathematics::Commutative AlgebraMathematics::Rings and AlgebrasZero (complex analysis)Field (mathematics)graded polynomial identity T_2-ideal graded codimensionsSuperalgebraSettore MAT/02 - AlgebraMathematics::Quantum AlgebraBounded functionMathematics::Representation TheoryLinear growthMathematicsJournal of Pure and Applied Algebra
researchProduct

Bounded elements of C*-inductive locally convex spaces

2013

The notion of bounded element of C*-inductive locally convex spaces (or C*-inductive partial *-algebras) is introduced and discussed in two ways: The first one takes into account the inductive structure provided by certain families of C*-algebras; the second one is linked to the natural order of these spaces. A particular attention is devoted to the relevant instance provided by the space of continuous linear maps acting in a rigged Hilbert space.

Discrete mathematicsPositive elementApplied Mathematics010102 general mathematicsMathematics - Operator AlgebrasRigged Hilbert spaceMathematics - Rings and AlgebrasLF-spaceSpace (mathematics)01 natural sciencesOperator spaceBounded operatorBounded elements Inductive limit of C*-algebras Partial *-algebras010101 applied mathematics47L60 47L40Rings and Algebras (math.RA)Bounded functionLocally convex topological vector spaceFOS: Mathematics0101 mathematicsOperator Algebras (math.OA)Mathematics
researchProduct

Identities of PI-Algebras Graded by a Finite Abelian Group

2011

We consider associative PI-algebras over an algebraically closed field of zero characteristic graded by a finite abelian group G. It is proved that in this case the ideal of graded identities of a G-graded finitely generated PI-algebra coincides with the ideal of graded identities of some finite dimensional G-graded algebra. This implies that the ideal of G-graded identities of any (not necessary finitely generated) G-graded PI-algebra coincides with the ideal of G-graded identities of the Grassmann envelope of a finite dimensional (G × ℤ2)-graded algebra, and is finitely generated as GT-ideal. Similar results take place for ideals of identities with automorphisms.

Discrete mathematicsPure mathematicsAlgebra and Number TheoryMathematics::Commutative AlgebraMathematics::Rings and AlgebrasGraded ringElementary abelian groupGraded Lie algebraFiltered algebraDifferential graded algebraIdeal (ring theory)Abelian groupAlgebraically closed fieldMathematicsCommunications in Algebra
researchProduct

Group algebras and Lie nilpotence

2013

Abstract Let ⁎ be an involution of a group algebra FG induced by an involution of the group G. For char F ≠ 2 , we classify the groups G with no 2-elements and with no nonabelian dihedral groups involved whose Lie algebra of ⁎-skew elements is nilpotent.

Discrete mathematicsPure mathematicsAlgebra and Number TheorySimple Lie group010102 general mathematicsMathematics::Rings and AlgebrasUniversal enveloping algebra0102 computer and information sciencesGroup algebraSkew-symmetric element01 natural sciencesRepresentation theoryLie conformal algebraGraded Lie algebraRepresentation of a Lie groupgroup algebra unit010201 computation theory & mathematicsLie nilpotentGroup algebra0101 mathematicsNilpotent groupANÉIS E ÁLGEBRAS ASSOCIATIVOSMathematicsJournal of Algebra
researchProduct

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
researchProduct

Multialternating graded polynomials and growth of polynomial identities

2012

Let G be a finite group and A a finite dimensional G-graded algebra over a field of characteristic zero. When A is simple as a G-graded algebra, by mean of Regev central polynomials we construct multialternating graded polynomials of arbitrarily large degree non vanishing on A. As a consequence we compute the exponential rate of growth of the sequence of graded codimensions of an arbitrary G-graded algebra satisfying an ordinary polynomial identity. In particular we show it is an integer. The result was proviously known in case G is abelian.

Discrete mathematicsPure mathematicsHilbert series and Hilbert polynomialMathematics::Commutative AlgebraApplied MathematicsGeneral MathematicsMathematics::Rings and AlgebrasGraded ringMathematics - Rings and AlgebrasGraded Lie algebramultialternating polynomialFiltered algebrasymbols.namesakeReciprocal polynomialRings and Algebras (math.RA)Differential graded algebraFactorization of polynomialssymbolsFOS: MathematicsElementary symmetric polynomial16R50 16P90 16R10 16W50Mathematics
researchProduct

Geometric properties of involutive distributions on graded manifolds

1997

AbstractA proof of the relative version of Frobenius theorem for a graded submersion, which includes a very short proof of the standard graded Frobenius theorem is given. Involutive distributions are then used to characterize split graded manifolds over an orientable base, and split graded manifolds whose Batchelor bundle has a trivial direct summand. Applications to graded Lie groups are given.

Discrete mathematicsPure mathematicsMathematics(all)Mathematics::Commutative AlgebraGeneral MathematicsMathematics::Rings and AlgebrasLie groupGraded Lie algebrasymbols.namesakeDifferential graded algebraBundlesymbolsMathematics::Differential GeometryFrobenius theorem (differential topology)MathematicsIndagationes Mathematicae
researchProduct