This note records the results of
an effort to understand in simple terms a certain theorem of Lichtenbaum and
Schlessinger: Let I ⊃ J be ideals of noetherian local ring. If I and I∕J are generated
by regular sequences, then so is J. This theorem is closely related to the well known:
If R and R∕P are regular local rings, then P is generated by part of a regular system
of parameters. We investigate the implications of “I∕J is generated by a regular
sequence” and discover an elementary theorem having both of these results as
corollaries.
