We study certain filtrations of indecomposable injective modules over
classical Lie superalgebras, applying a general approach for noetherian rings
developed by Brown, Jategaonkar, Lenagan, and Warfield. To indicate the
consequences of our analysis, suppose that g is a complex classical simple
Lie superalgebra and that E is an indecomposable injective g-module with
nonzero (and so necessarily simple) socle L. (Recall that every essential
extension of L, and in particular every nonsplit extension of L by a simple
module, can be formed from g-subfactors of E.) A direct transposition of
the Lie algebra theory to this setting is impossible. However, we are able to
present a finite upper bound, easily calculated and dependent only on g, for
the number of isomorphism classes of simple highest weight g-modules
appearing as g-subfactors of E.Comment: 20 page