algebra, a module M over a ring R is called torsionless if it can be embedded into some direct product RI. Equivalently, M is torsionless if each non-zero...

R-modules preserves exactness. Torsionless A module is called torsionless if it embeds into its algebraic dual. Simple A simple module S is a module that...

is one for which the canonical homomorphism is an isomorphism. A torsionless module is one for which the canonical homomorphism is injective. Example:...

a module over k[x, y]. Any torsionless module over a domain is a torsion-free module, but the converse is not true, as Q is a torsion-free Z-module that...

topological module Tor Tor functor torsion-free torsion-free module torsionless torsionless module uniform A uniform module is a module in which every...

to a dual module. There is still a canonical evaluation map, but it is not always injective; if it is, this is known as a torsionless module; if it is...

(dualizing sheaf) on a normal projective variety is a divisorial sheaf. Torsionless module Torsion sheaf Twisted sheaf Hartshorne 1980, Corollary 1.2. Hartshorne...

functors of the tensor product. 6.  A torsionless module is a module isomorphic to a submodule of a free module. total The total ring of fractions or...

torsion-free R-module is flat. Every torsionless R-module is flat. Every ideal of R is flat Every overring of R is R-flat Every submodule of a flat R-module is flat...