| 程福长.Λ-模的σ-子模的标准表示式[J].数学研究及应用,1983,3(4):17~23 |
| Λ-模的σ-子模的标准表示式 |
| Normal Expression of σ-Submodttle of the Λ-Module |
| 投稿时间：1981-09-12 |
| DOI：10.3770/j.issn:1000-341X.1983.04.005 |
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| Let A be a commutative ring with unit element, and let M be a Λ-module and σ∈HomΛ (M, M). Then a non-empty subset N of M is called a σ-submodule of the Λ-module M, if (1) a-b∈N for all a, bg∈N, and (2) λσ(α)∈N and x-σ(x)∈N for all λ∈Λ, α∈N, x∈M. Let N be a σ-submodule of M. N is said to be a primary σ-submodule of the Λ-module M, if (1) N≠M, and (2) whenever λ∈Λ, x∈M and λσ(x) ∈N, then either x∈N or λkσ(M)?N for some positive integer h. This paper is intended to show (1) that if M satisfies maximal condition of σ-submodule, and K is a σ-submodule of M, then K is a finite intersection of primary σ-submodules, and (2) that the uniqueness on the normal expression of σ-submodule of the Λ-module. Also, some results of fractional module have been obtained. |
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