Unimodular element
From Encyclopedia of Mathematics
unimodular vector
Let be a ring with unit and
a right module over
. An element
in
is called unimodular if
and the submodule
generated by
has a complement
in
, i.e. there is a submodule
such that
,
, so that
.
An element of a free module that is part of a basis of
is unimodular. An element
is unimodular if and only if there is a homomorphism of modules
such that
. A row (or column) of a unimodular matrix over
is unimodular. The question when the converse is true is important in algebraic
-theory. Cf. also Stable rank.
References
[a1] | A.J. Hahn, O.T. O'Meara, "The classical groups and ![]() |
How to Cite This Entry:
Unimodular element. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Unimodular_element&oldid=24134
Unimodular element. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Unimodular_element&oldid=24134