On the Krull dimension of endo-bounded modules

Authors: AHMAD HAGHANY, MAJID MAZROOEI, MOHAMAD REZA VEDADI

Abstract: Modules in which every essential submodule contains an essential fully invariant submodule are called endo-bounded. Let M be a nonzero module over an arbitrary ring R and X = Spec_2(M_R), the set of all fully invariant L_2-prime submodules of M_R. If M_R is a quasi-projective L_2-Noetherian such that (M/P)_R is endo-bounded for any P \in X, then it is shown that the Krull dimension of M_R is at most the classical Krull dimension of the poset X. The equality of these dimensions and some applications are obtained for certain modules. This gives a generalization of a well-known result on right fully bounded Noetherian rings.

Keywords: Classical Krull dimension, endo-bounded module, FBN ring, Krull dimension, L_2-Noetherian module, L_2-prime module

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