ABSTRACT
Let ℙ (R-sp) be the boolean lattice of subsets of R-sp. For each left R-module M, we define the assassin ass(M) of M to be {Π ∈ R-sp | M has a π-cocritical submodule}. By [16, Proposition 21.1] we see that ass(_) is a quasidecomposition function on R-mod with values in ℙ (R-sp). This function is a predecomposition function if and only if R is a left definite ring. In particular, ass(_) is a predecomposition function whenever R is left noetherian.
