Math 721
Spring 2001
Homework 1
These problems will be due shortly after I arrive back. Please begin reading the sections in Hungerford’s book on modules and attempt to answer them.
a)
If
then show that
is an ideal of
(If
then we say that
is a torsion element of
)
b)
If
is an integral domain
and
is the set of torsion
elements of
, show that
is a submodule of
c)
Is
b) true if “integral domain” is omitted?