Multiplication modules with Krull dimension

Behboodi, Mahmood; Molakarimi, Maryam

doi:10.3906/mat-1101-63

Turkish Journal of Mathematics

2012

DOI: 10.3906/mat-1101-63

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Multiplication modules with Krull dimension

Mahmood Behboodi¹,

Maryam Molakarimi²

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2013

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On the Krull dimension of endo-bounded modules

Haghany¹,

Mazrooei²,

Vedadi³

2013

Turk J Math

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Modules in which every essential submodule contains an essential fully invariant submodule are called endobounded. Let M be a nonzero module over an arbitrary ring R and X = Spec 2 (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 ∈ 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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On the Krull dimension of endo-bounded modules

Haghany¹,

Mazrooei²,

Vedadi³

2013

Turk J Math

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Multiplication modules with Krull dimension

Cited by 1 publication

References 8 publications

On the Krull dimension of endo-bounded modules

On the Krull dimension of endo-bounded modules

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