-
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...
- 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...
-
module is one for
which the
canonical homomorphism is an isomorphism. A
torsionless module is one for
which the
canonical homomorphism is injective. Example:...
- b}^{a}=0.} The
difference between a
connection with torsion, and the
unique torsionless connection is
given by the
contorsion tensor.
Connections with torsion...
- }=A_{\beta }R^{\beta }{}_{\nu \rho \sigma }\,,}
since the
connection is
torsionless,
which means that the
torsion tensor vanishes. This can be generalized...
- turn it into a Levi-Civita connection, i.e. to make a
connection be
torsionless. Indeed, if one
writes θ for the
solder form, then the
torsion tensor...
- (dualizing sheaf) on a
normal projective variety is a
divisorial sheaf.
Torsionless module Torsion sheaf Twisted sheaf Hartshorne 1980,
Corollary 1.2. Hartshorne...
- Einstein–Hilbert and Rarita–Schwinger
actions now
being written with a
torsionless spin
connection that
explicitly depends on the vielbeins. The supersymmetry...
-
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...
