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...

a ring Torsion-free module, in algebra See also Torsion-free (disambiguation) Analytic torsion (Reidemeister torsion, R-torsion, Franz torsion, de Rham...

torsion subgroup makes torsion-free abelian groups into a reflective subcategory. Torsion (algebra) Torsion-free abelian group Torsion abelian group Serge...

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...

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...

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...

algebra Magma object Torsion (algebra) Symbolic mathematics Finite field arithmetic Gröbner basis Buchberger's algorithm List of commutative algebra topics...

In algebraic geometry and number theory, the torsion conjecture or uniform boundedness conjecture for torsion points for abelian varieties states that...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

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...

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...

unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties...

same for compact Riemannian manifolds. Reidemeister torsion was the first invariant in algebraic topology that could distinguish between closed manifolds...

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...

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...

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...

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...

In mathematics, an Albert algebra is a 27-dimensional exceptional Jordan algebra. They are named after Abraham Adrian Albert, who pioneered the study of...

In algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion-free modules. Formally, a module M over...

decidable. Most algebraic structures other than Boolean algebras are undecidable. There are still many areas of current research: Amongst torsion-free abelian...

K-theory. The earliest application of algebraic K-theory to topology was Whitehead's construction of Whitehead torsion. A closely related construction was...

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...

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...

(1979). "Torsion algebraic cycles and a theorem of Roitman". Compositio Mathematica. 39 (1). MR 0539002. Milne, J. S. (1982). "Zero cycles on algebraic varieties...

mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered...

In mathematics, an Azumaya algebra is a generalization of central simple algebras to R {\displaystyle R} -algebras where R {\displaystyle R} need not...

In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes. For...

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...

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}}...

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...