On the Krull dimension of endo-bounded modules

Authors : Ahmad Haghany, Majid Mazrooei, Mohammad Reza Vedadi

Pages : 925-933

Doi:10.3906/mat-1206-31

View : 13 | Download : 10

Publication Date : 9999-12-31

Article Type : Makaleler

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 = Spec2(MR), the set of all fully invariant L2-prime submodules of MR. If MR is a quasi-projective L2-Noetherian such that (M/P)R is endo-bounded for any P \in X, then it is shown that the Krull dimension of MR 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, L2-Noetherian module, L2-prime module