Search results for "Finitely-generated abelian group"

showing 8 items of 18 documents

A finiteness condition for finitely generated semigroups

1984

Pure mathematicsAlgebra and Number TheoryFinitely-generated abelian groupAlgebra over a fieldMathematics
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From Bi-ideals to Periodicity

2008

The necessary and sufficient conditions are extracted for periodicity of bi-ideals. They cover infinitely and finitely generated bi-ideals.

Pure mathematicsIdeal (set theory)Mathematics::Commutative AlgebraGeneral MathematicsCalculusCover (algebra)Finitely-generated abelian groupSoftwareWord (computer architecture)Computer Science ApplicationsMathematicsRAIRO - Theoretical Informatics and Applications
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On cubic elliptic varieties

2013

Let X->P^(n-1) be an elliptic fibration obtained by resolving the indeterminacy of the projection of a cubic hypersurface Y of P^(n+1) from a line L not contained in Y. We prove that the Mordell-Weil group of the elliptic fibration is finite if and only if the Cox ring of X is finitely generated. We also provide a presentation of the Cox ring of X when it is finitely generated.

Pure mathematicsMathematics::Commutative AlgebraGroup (mathematics)Applied MathematicsGeneral MathematicsFibrationMathematics - Algebraic GeometryHypersurfaceMathematics::Algebraic GeometryProjection (mathematics)Line (geometry)14C20 14DxxFOS: MathematicsMathematics (all)Finitely-generated abelian groupSettore MAT/03 - GeometriaCox ringAlgebraic Geometry (math.AG)Mathematics
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A characterization of fundamental algebras through S-characters

2020

Abstract Fundamental algebras play an important role in the theory of algebras with polynomial identities in characteristic zero. They are defined in terms of multialternating polynomials non vanishing on them. Here we give a characterization of fundamental algebras in terms of representations of symmetric groups obtaining this way an equivalent definition. As an application we determine when a finitely generated Grassmann algebra is fundamental.

Pure mathematicsPolynomialAlgebra and Number Theory010102 general mathematicsZero (complex analysis)Characterization (mathematics)01 natural sciencesSymmetric group0103 physical sciences010307 mathematical physicsFinitely-generated abelian group0101 mathematicsExterior algebraREPRESENTAÇÃO DE GRUPOS SIMÉTRICOSMathematicsJournal of Algebra
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On multiplicities of cocharacters for algebras with superinvolution

2021

Abstract In this paper we deal with finitely generated superalgebras with superinvolution, satisfying a non-trivial identity, whose multiplicities of the cocharacters are bounded by a constant. Along the way, we prove that the codimension sequence of such algebras is polynomially bounded if and only if their colength sequence is bounded by a constant.

Pure mathematicsSequenceMultiplicitiesAlgebra and Number TheoryMathematics::Commutative AlgebraSuperinvolution010102 general mathematicsCodimensionCocharacters; Colength; Multiplicities; SuperinvolutionCocharacters01 natural sciencesmultiplicitiecocharacterSettore MAT/02 - AlgebraIdentity (mathematics)SuperinvolutionBounded function0103 physical sciences010307 mathematical physicsFinitely-generated abelian groupColength0101 mathematicsConstant (mathematics)Mathematics
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Homogeneous actions on the random graph

2018

We show that any free product of two countable groups, one of them being infinite, admits a faithful and homogeneous action on the Random Graph. We also show that a large class of HNN extensions or free products, amalgamated over a finite group, admit such an action and we extend our results to groups acting on trees. Finally, we show the ubiquity of finitely generated free dense subgroups of the automorphism group of the Random Graph whose action on it have all orbits infinite.

Random graphFinite group20B22 (primary) 20E06 20E05 05C63 54E52 (secondary)Group Theory (math.GR)Homogeneous actions16. Peace & justicegroups acting on trees[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]Action (physics)CombinatoricsMathematics::Group TheoryFree productHomogeneousBaire category theoremFOS: MathematicsDiscrete Mathematics and CombinatoricsCountable setBaire category theoremfree groupsGeometry and TopologyFinitely-generated abelian groupMathematics - Group TheoryMSC: 20B22 (primary); 20E06 20E05 05C63 54E52 (secondary)random graphMathematicsGroups, Geometry, and Dynamics
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Triangular irreducibility of congruences in quasivarieties

2014

Certain forms of irreducibility as well as of equational definability of relative congruences in quasivarieties are investigated. For any integer \({m \geqslant 3}\) and a quasivariety Q, the notion of an m-triangularily meet-irreducible Q-congruence in the algebras of Q is defined. In Section 2, some characterizations of finitely generated quasivarieties involving this notion are provided. Section 3 deals with quasivarieties with equationally definable m-triangular meets of relatively principal congruences. References to finitely based quasivarieties and varieties are discussed.

Section (fiber bundle)Mathematics::LogicPure mathematicsAlgebra and Number TheoryQuasivarietyIntegerMathematics::General MathematicsMathematics::Rings and AlgebrasMathematics::General TopologyIrreducibilityFinitely-generated abelian groupCongruence relationMathematicsAlgebra Universalis
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More on Finitely Generated Quasivarieties

2015

We begin with the following observation concerning arbitrary finitely generated quasivarieties

Subdirect productMathematics::LogicPure mathematicsMathematics::General MathematicsMathematics::Rings and AlgebrasMathematics::General TopologyFinitely-generated abelian groupMathematics
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