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.
Classical Krull dimension, endo-bounded module, FBN ring, Krull dimension, L_2-Noetherian module, L_2-prime module
HAGHANY, AHMAD; MAZROOEI, MAJID; and VEDADI, MOHAMAD REZA
"On the Krull dimension of endo-bounded modules,"
Turkish Journal of Mathematics: Vol. 37:
6, Article 4.
Available at: https://journals.tubitak.gov.tr/math/vol37/iss6/4