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Abstract

This work studies the concept of En-prime compactly packed (πΈπ‘›βˆ’π’«.𝒸.𝒫) modules. Some properties and characterizations have been studied. Put β‚© is an Π―-module and every submodule is En-pure , then β‚© is πΈπ‘›βˆ’π’«.𝒸.𝒫 if and only if each proper submodule Ο’ of β‚© is cyclic, If β‚© is πΈπ‘›βˆ’π’«.𝒸.𝒫. β‚© which has at least one maximal submodule then β‚© satisfies the ACC on En-p-radical submodule. The generalization of this idea has been given for S-Acts. if for each family {PΞ±}α∈λ of En-prime subact of Π” with Ρͺ βŠ†β‹ƒPαα∈λ, ΡͺβŠ†PΞ² for some β∈λ. An S-Act Π” is πΈπ‘›βˆ’π’«.𝒸.𝒫, if every subact is πΈπ‘›βˆ’π’«.𝒸.𝒫. Various properties of πΈπ‘›βˆ’π’«.𝒸.𝒫 modules and S-Acts have been studied, like, β‚© is an R-module and every submodule is En-pure, then β‚© is πΈπ‘›βˆ’π’«.𝒸.𝒫 if and only if each proper submodule Ο’ of β‚© is cyclic. The general is, if Π” is πΈπ‘›βˆ’π’«.𝒸.𝒫 S-Act which has at least one maximal subact then Π” satisfies the ACC on En-p-radical subact.and suppose that Π” is an πΈπ‘›βˆ’π’«.𝒸.𝒫 S-Act. If the CST is satisfied for Π”, then dim Д≀1, and prove that, If Π” is a multiplication S-Act that satisfies the ACC on En-p- radical subact, then for every proper subact Ρͺ of Π” there exists a finite number of minimal En-prime subact of Ρͺ. Let f: Д→Д’ be an epimorphism. If Π” is πΈπ‘›βˆ’π’«.𝒸.𝒫 then so is Д’. The converse is true when Π” is finitely generated or (multiplication) S-Act and kerfβŠ†rad{0}.

Keywords

En-prime subacts, En-prime submodules, En-pure subacts, En-prime compactly packed S-act, Multiplication S-act

Subject Area

Mathematics

Article Type

Article

First Page

1630

Last Page

1634

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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