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...

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

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

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...

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...

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...

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

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

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...

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...

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...

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

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...

in a Noetherian ring R, then the Rees algebra of I is the quotient of the symmetric algebra of I by its torsion submodule. The associated graded ring...

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...

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

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...

operation Steenrod algebra Bott periodicity theorem K-theory Topological K-theory Adams operation Algebraic K-theory Whitehead torsion Twisted K-theory...

the tensor product, and feature strongly in homological algebra. The name comes from the torsion subgroup in abelian group theory. Symbolic method of invariant...

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...

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...

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

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

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

finite CW-complexes being a simple homotopy equivalence is its Whitehead torsion τ ( f ) {\displaystyle \tau (f)} which is an element in the Whitehead group...

Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations...

glossary of commutative algebra. See also list of algebraic geometry topics, glossary of classical algebraic geometry, glossary of algebraic geometry, glossary...