Torsion-free: Difference between revisions

Content deleted Content added

Inline

Latest revision as of 08:53, 27 August 2016

In mathematics, torsion-free may refer to:

Torsion-free group, a group whose only element of finite order is the identity
Torsion-free module, module over an integral 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 of a maximal linearly independent subset of an abelian group or of a module over an integral domain

Torsion-free affine connection, an affine connection whose torsion tensor vanishes
Torsion-free metric connection or Levi-Civita connection, a unique symmetric connection on the tangent bundle of a manifold compatible with the metric

@@ Line 1: / Line 1: @@
-In [[mathematics]], the term '''torsion-free''' may refer to several unrelated notions:
+In [[mathematics]], '''torsion-free''' may refer to:
-* In [[abstract algebra]], a [[group (mathematics)|group]] is [[torsion (algebra)|torsion-free]] if the only element of finite order is the identity.
+== Abstract algebra ==
-* In [[differential geometry]], an [[affine connection]] is torsion-free if its [[torsion tensor]] vanishes.
+* [[Torsion-free group]], a group whose only element of finite order is the identity
+* [[Torsion-free module]], module over an integral 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 of a maximal linearly independent subset of an abelian group or of a module over an integral domain
+== Differential geometry ==
+* Torsion-free affine connection, an affine connection whose [[torsion tensor]] vanishes
+* Torsion-free metric connection or [[Levi-Civita connection]], a unique symmetric connection on the tangent bundle of a manifold compatible with the metric
+== See also ==
+* [[Torsion (disambiguation)]]
 {{mathdab}}