L-2-PRIME AND DIMENSIONAL MODULES

We introduce a map that generalizes Krull and Noetherian dimensions. If M-R finitely generates all fully invariant submodules and has acc on them, there are only a finite number of minimal L-2-prime submodules P-i(1 <= i <= m) and when defined, k(M) = k(M/P-j) for some j. Here, each M/P-i is a prime R-module, and in particular, M has finite length if every irreducible prime submodule of M is maximal. Quasi-projective L-2-prime R-module with non-zero socle are investigated and some applications are then given when k(M) means the Krull dimension or the injective dimension.