Constructions of finitely generated submodules of constructively noetherian modules

Let $R$ be a commutative ring with non-zero identity. Various properties of multiplication modules are considered. We generalize Ohm’s properties for submodules of a finitely generated faithful multiplication $R$ -module (see [8], [12] and [3]).

Maximal elements of support.

Yassemi, S. (1998)

Acta Mathematica Universitatis Comenianae. New Series

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Skew polynomial rings satisfying $r$ - $B n d$ property.

Salem, Refaat M. (1994)

Portugaliae Mathematica

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Upper bounds for the cohomological dimensions of finitely generated modules over a commutative Noetherian ring

Ghader Ghasemi, Kamal Bahmanpour, Jafar A'zami (2014)

Colloquium Mathematicae

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Let R be a commutative Noetherian ring, I a proper ideal of R, and M be a finitely generated R-module. We provide bounds for the cohomological dimension of the R-module M with respect to the ideal I in several cases.

On some properties of $\oplus$ -supplemented modules.

Idelhadj, A., Tribak, R. (2003)

International Journal of Mathematics and Mathematical Sciences

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Cohen-Macaulayness of multiplication rings and modules

R. Naghipour, H. Zakeri, N. Zamani (2003)

Colloquium Mathematicae

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Let R be a commutative multiplication ring and let N be a non-zero finitely generated multiplication R-module. We characterize certain prime submodules of N. Also, we show that N is Cohen-Macaulay whenever R is Noetherian.