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Flashcards

Abstract Algebra Definitions

Carlos Figueroa Inglês 5,0Avaliação média 5,0 de 5 (1 avaliação) 79 flashcards

Abstract Algebra Definitions

Flashcards do conjunto (79)

  1. 1Order of permutationthe order of a permutation is the l.c.m. of the lengths of the cycles in its cycle decomposition.
  2. 2Binary operation Associative CommutativeBinary operation Associative Commutative
  3. 3Stabilizer of s in Gif G is a group acting on a set S and s is some fixed element of S, the stabilizer of s in G is the
    set    Stabilizer of s in G
  4. 4GroupA group is an order pair (G, *) where G is a set and * is a binary operation on G satisfying the following axioms:Group
  5. 5Zero divisor & Unit in RZero divisor & Unit in R
  6. 6Sylow's Theorem (formal)Sylow's Theorem (formal)
  7. 7Transposition (cycles)Transposition (cycles)
  8. 8Symmetric group on the set Omega Permutations of OmegaSymmetric group on the set Omega Permutations of Omega
  9. 9Third Isomorphism Theorem (groups)Third Isomorphism Theorem (groups)
  10. 10Unique Factorization Domain (U.F.D)Unique Factorization Domain (U.F.D)
  11. 11Subgroup of G generated by ASubgroup of G generated by A
  12. 12SubringSubring
  13. 13SubgroupSubgroup
  14. 14Sylow TheoremSylow Theorem
  15. 15Sum, Product, Power of Ideals ISum, Product, Power of Ideals I
  16. 16Solvable groupsSolvable groups
  17. 17Sign of sigma Even and Odd PermutationsSign of sigma Even and Odd Permutations
  18. 18Simple groupsSimple groups
  19. 19Second isomorphism theorem (groups)Second isomorphism theorem (groups)
  20. 20RelationsRelations
  21. 21Quotient group or Factor groupQuotient group or Factor group
  22. 22Quotient RingQuotient Ring
  23. 23RingRing
  24. 24Second Isomorphism Theorem for RingsSecond Isomorphism Theorem for Rings
  25. 25Presentation of GPresentation of G
  26. 26Principal Ideal Domain (P.I.D)Principal Ideal Domain (P.I.D)
  27. 27Prime IdealPrime Ideal
  28. 28Quaternion Group Q_8Quaternion Group Q_8
  29. 29P-groups & Sylow p-subgroupsP-groups & Sylow p-subgroups
  30. 30Orbit of G & Transitive actionOrbit of G & Transitive action
  31. 31Order (element)Order (element)
  32. 32Norm & Positive NormNorm & Positive Norm
  33. 33Natural Projection (homomorphism) of G onto G/NNatural Projection (homomorphism) of G onto G/N
  34. 34Normalizer of A in GNormalizer of A in G
  35. 35Length of a CylceLength of a Cylce
  36. 36Lattice of Subgroups of Q_8Lattice of Subgroups of Q_8
  37. 37Left and Right CosetsLeft and Right Cosets
  38. 38Maximal IdealMaximal Ideal
  39. 39Left, Right, Two-sided IdealLeft, Right, Two-sided Ideal
  40. 40Lattice of D_8Lattice of D_8
  41. 41Lagrange's TheoremLagrange's Theorem
  42. 42Lattice of S_3Lattice of S_3
  43. 43Klein 4 GroupKlein 4 Group
  44. 44Lattice of D_16Lattice of D_16
  45. 45Integral DomainIntegral Domain
  46. 46Kernel of a Homomorphism \rhoKernel of a Homomorphism \rho
  47. 47Kernel of an ActionKernel of an Action
  48. 48IsomorphismIsomorphism
  49. 49Irreducible, Prime, and Associate elementIrreducible, Prime, and Associate element
  50. 50Homomorphism (groups)Homomorphism (groups)
  51. 51Inner automorphismInner automorphism
  52. 52Index of H in GIndex of H in G
  53. 53Ideal generated by AIdeal generated by A
  54. 54FieldField
  55. 55First Isomorphism Theorem (groups)First Isomorphism Theorem (groups)
  56. 56Group ActionGroup Action
  57. 57First Isomorphism Theorem for RingsFirst Isomorphism Theorem for Rings
  58. 58Fourth Isomorphism Theorem (Groups)Fourth Isomorphism Theorem (Groups)
  59. 59Euclidean DomainEuclidean Domain
  60. 60Division RingDivision Ring
  61. 61Fibers of \rhoFibers of \rho
  62. 62Cycle type of \sigma & Partition of nCycle type of \sigma & Partition of n
  63. 63cyclic groupcyclic group
  64. 64Cycle decomposition of \sigmaCycle decomposition of \sigma
  65. 65Conjugate (element , set) & Normal groupConjugate (element , set) & Normal group
  66. 66Conjugate (subsets)Conjugate (subsets)
  67. 67Conjugate (elements)Conjugate (elements)
  68. 68Class EquationClass Equation
  69. 69Binary operationBinary operation
  70. 70Cauchy's TheoremCauchy's Theorem
  71. 71Cayley's TheoremCayley's Theorem
  72. 72CycleCycle
  73. 73Composition SeriesComposition Series
  74. 74Center of GCenter of G
  75. 75Characteristic in GCharacteristic in G
  76. 76Centralizer of A in GCentralizer of A in G
  77. 77Alternating groupAlternating group
  78. 78Automorphism of GAutomorphism of G
  79. 79Alternating Group ExampleAlternating Group Example

Informações

Descrição
FlashCards sobre Abstract Algebra Definitions, criado por Carlos Figueroa em 05-06-2018.
Criado por
Carlos Figueroa · jun 2018
Atualizado
9 jun 2018
Visualizações
43
Avaliação
Avaliação média 5,0 de 5 (1 avaliação)

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