The theory of inelastic electron resonant tunneling through a double-b
arrier nanostructure is extended to establish a theory of phonon-assis
ted resonant magnetotunneling when a magnetic field is applied paralle
l to the tunneling current. At higher temperatures we have discovered
an interesting characteristic oscillation of the width and height of t
he main peak in the I-V curve when the ratio omega0/omega(c) changes b
etween integer (double resonant) and half integer (single resonant), w
here omega0 is the LO phonon frequency and omega(c) is the cyclotron f
requency in the well. If confirmed experimentally, our theoretical pre
diction provides an additional method to determine the electronic effe
ctive mass in the well.