On the Krull dimension of endo-bounded modules | Zendy

A. Haghany | Zendy; Majid Mazrooei | Zendy; M. R. Vedadi | Zendy

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On the Krull dimension of endo-bounded modules

Author(s) -

A. Haghany,

Majid Mazrooei,

M. R. Vedadi

Publication year - 2013

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1206-31

Subject(s) - mathematics , krull dimension , bounded function , global dimension , noetherian , invariant (physics) , pure mathematics , regular local ring , dimension (graph theory) , discrete mathematics , generalization , combinatorics , algebra over a field , mathematical analysis , mathematical physics

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.

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