-
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
element of...
- any
exact sequence of R-modules
preserves exactness.
Torsionless A
module is
called torsionless if it
embeds into its
algebraic dual.
Simple A simple...
-
module is one for
which the
canonical homomorphism is an isomorphism. A
torsionless module is one for
which the
canonical homomorphism is injective. Example:...
- 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 is not
torsionless. Over...
- }=A_{\beta }R^{\beta }{}_{\nu \rho \sigma }\,,}
since the
connection is
torsionless,
which means that the
torsion tensor vanishes. This can be generalized...
- (dualizing sheaf) on a
normal projective variety is a
divisorial sheaf.
Torsionless module Torsion sheaf Twisted sheaf Hartshorne 1980,
Corollary 1.2. Hartshorne...
-
evaluation map, but it is not
always injective; if it is, this is
known as a
torsionless module; if it is an isomophism, the
module is
called reflexive. For topological...
-
topological module Tor Tor
functor torsion-free torsion-free
module torsionless torsionless module uniform A
uniform module is a
module in
which every two...
-
localizations of R
Flatness Every 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...
- b}^{a}=0.} The
difference between a
connection with torsion, and the
unique torsionless connection is
given by the
contorsion tensor.
Connections with torsion...
