• ring theory, a torsion element is an element of a module that yields zero when multiplied by some non-zero-divisor of the ring. The torsion submodule of...
    12 KB (1,660 words) - 18:12, 1 December 2024
  • a ring Torsion-free module, in algebra See also Torsion-free (disambiguation) Analytic torsion (Reidemeister torsion, R-torsion, Franz torsion, de Rham...
    2 KB (226 words) - 14:35, 19 January 2024
  • torsion subgroup makes torsion-free abelian groups into a reflective subcategory. Torsion (algebra) Torsion-free abelian group Torsion abelian group Serge...
    7 KB (924 words) - 00:02, 6 December 2024
  • Thumbnail for Torsion-free abelian group
    mathematics, specifically in abstract algebra, a torsion-free abelian group is an abelian group which has no non-trivial torsion elements; that is, a group in...
    6 KB (783 words) - 23:28, 15 December 2023
  • In algebra, a torsion-free module is a module over a ring such that zero is the only element annihilated by a regular element (non zero-divisor) of the...
    4 KB (597 words) - 13:20, 10 November 2024
  • order. A torsion-free abelian group is an abelian group in which the identity element is the only element with finite order. Torsion (algebra) Jordan–Schur...
    5 KB (635 words) - 15:06, 31 August 2024
  • algebra Magma object Torsion (algebra) Symbolic mathematics Finite field arithmetic Gröbner basis Buchberger's algorithm List of commutative algebra topics...
    12 KB (1,129 words) - 10:50, 10 October 2024
  • In algebraic geometry and number theory, the torsion conjecture or uniform boundedness conjecture for torsion points for abelian varieties states that...
    12 KB (1,411 words) - 14:57, 31 August 2024
  • Thumbnail for Exterior algebra
    In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...
    77 KB (12,138 words) - 00:30, 22 November 2024
  • domain where zero is the only torsion element Torsion-free abelian group, an abelian group which is a torsion-free group Torsion-free rank, the cardinality...
    817 bytes (140 words) - 08:53, 27 August 2016
  • Thumbnail for Torsion tensor
    In differential geometry, the torsion tensor is a tensor that is associated to any affine connection. The torsion tensor is a bilinear map of two input...
    27 KB (4,371 words) - 18:19, 16 December 2024
  • Thumbnail for Hodge conjecture
    Hodge conjecture (category Algebraic geometry)
    unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties...
    23 KB (3,002 words) - 08:25, 13 December 2024
  • In abstract algebra, a torsion abelian group is an abelian group in which every element has finite order. For example, the torsion subgroup of an abelian...
    459 bytes (48 words) - 08:28, 4 August 2020
  • Tor functor (redirect from Torsion functor)
    associative algebras can all be defined in terms of Tor. The name comes from a relation between the first Tor group Tor1 and the torsion subgroup of an...
    13 KB (2,030 words) - 16:56, 21 August 2024
  • has no basis and no rank, in the usual sense of linear algebra. However this module has a torsion-free rank equal to 1. If R is any ring and n a natural...
    22 KB (2,984 words) - 12:42, 15 December 2024
  • same for compact Riemannian manifolds. Reidemeister torsion was the first invariant in algebraic topology that could distinguish between closed manifolds...
    14 KB (2,129 words) - 08:30, 2 August 2024
  • In mathematics, an Albert algebra is a 27-dimensional exceptional Jordan algebra. They are named after Abraham Adrian Albert, who pioneered the study of...
    7 KB (717 words) - 05:52, 2 December 2024
  • Thumbnail for Abelian group
    decidable. Most algebraic structures other than Boolean algebras are undecidable. There are still many areas of current research: Amongst torsion-free abelian...
    36 KB (5,284 words) - 13:55, 8 December 2024
  • In algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion-free modules. Formally, a module M over...
    30 KB (4,590 words) - 03:05, 9 August 2024
  • the module is a torsion module, which happens if and only if the support has dimension at most 1. Many of the modules over this algebra that occur in Iwasawa...
    9 KB (1,182 words) - 08:57, 7 November 2023
  • K-theory. The earliest application of algebraic K-theory to topology was Whitehead's construction of Whitehead torsion. A closely related construction was...
    76 KB (10,397 words) - 06:16, 16 December 2024
  • always a torsion group. According to the Artin–Wedderburn theorem a finite-dimensional simple algebra A is isomorphic to the matrix algebra M(n,S) for...
    8 KB (1,134 words) - 04:54, 10 December 2024
  • In mathematics, the tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any rank) with multiplication being the...
    23 KB (4,160 words) - 15:09, 12 January 2024
  • (1979). "Torsion algebraic cycles and a theorem of Roitman". Compositio Mathematica. 39 (1). MR 0539002. Milne, J. S. (1982). "Zero cycles on algebraic varieties...
    7 KB (989 words) - 14:01, 25 August 2022
  • Thumbnail for Arithmetic geometry
    mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered...
    15 KB (1,464 words) - 19:56, 6 May 2024
  • In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes. For...
    16 KB (2,508 words) - 21:47, 29 October 2024
  • In mathematics, an Azumaya algebra is a generalization of central simple algebras to R {\displaystyle R} -algebras where R {\displaystyle R} need not...
    17 KB (3,208 words) - 22:29, 28 October 2023
  • integers of an algebraic number field K {\displaystyle K} is the ring of all algebraic integers contained in K {\displaystyle K} . An algebraic integer is...
    8 KB (1,054 words) - 02:09, 12 December 2024
  • case A is hereditary (i.e. B is a tilted algebra), the global dimension of B is at most 2, and the torsion pair ( X , Y ) {\displaystyle ({\mathcal {X}}...
    14 KB (1,690 words) - 01:23, 26 January 2024
  • Thumbnail for Transpose
    Transpose (category Abstract algebra)
    In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of...
    20 KB (2,525 words) - 18:28, 11 December 2024