Prime Submodule

In this paper we introduce the notion of bounded modules and fully bounded modules. A right R-module M is called a bounded module if every essential submodule of M contains a fully invariant submodule of M which is essential in MR. A module M is called a fully bounded module if M/X is bounded for any prime submodule X of M.

7p nguaconbaynhay11 07-04-2021 11 2   Download

In this paper, study nearly prime submodules and their properties as an extension of prime submodules.

6p trinhthamhodang1218 18-03-2021 6 1   Download

We investigate the relations between a radical submodule N of a module M being a finite intersection of prime submodules of M and the factor module M/N having finite uniform dimension. It is proved that if N is a radical submodule of a module M over a ring R such that M/N has finite uniform dimension, then N is a finite intersection of prime submodules.

16p danhdanh27 07-01-2019 21 1   Download

In this paper we prove the lying over and going down theoremsfor modules. Finally, we apply the above theorems and prove some results on the dimension of a module and itssubmodule.

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In this paper we introduce the concept of primary finitely compactly packed modules, which generalizes the concept of primary compactly packed modules. We first find the conditions that make the primary finitely compactly packed modules primary compactly packed.

10p danhdanh27 07-01-2019 19 2   Download

Let G be a multiplicative group. Let R be a G-graded commutative ring and M a G-graded R-module. Various properties of graded prime submodules and graded primary submodules of M are discussed. We have also discussed the graded radical of graded submodules of multiplication graded R-modules.

9p tuongvidanh 06-01-2019 13 1   Download

In this paper, the authors prove that every representable module over a commutative ring with identity satisfies the radical formula. With this result, they extend the class of modules satisfying the radical formula from that of Artinian modules to a larger one. They conclude their work by giving a description of the radical of a submodule of a representable module.

7p tuongvidanh 06-01-2019 17 2   Download