I-Rad——⊕补充模块

IF 0.6 Q3 MATHEMATICS

Acta Universitatis Sapientiae-Mathematica Pub Date : 2019-08-01 DOI:10.2478/ausm-2019-0017

B. Türkmen

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引用次数: 1

摘要

设M为一个r -模，I为r的一个理想。设M为I-Rad-⊕-补充，设M的每一个子模N，存在M的一个直接和K，使得M = N + K, N∩K≤K≤K。本文的目的是展示I-Rad-⊕-补充模的新性质。特别地，我们证明了任何I-Rad-⊕补模的有限直和都是I-Rad-⊕补模。我们还证明了当且仅当K和MK ${M \ / K}$对于M的完全不变直求和K是I-Rad-⊕补时，r模M是I-Rad-⊕补。最后，我们确定了离散赋值环上I-Rad-⊕补模的结构。

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I-Rad-⊕-supplemented modules

Abstract Let M be an R-module and I be an ideal of R. We say that M is I-Rad-⊕-supplemented, provided for every submodule N of M, there exists a direct summand K of M such that M = N + K, N ∩ K ⊆ IK and N ∩ K Rad(K). The aim of this paper is to show new properties of I-Rad-⊕-supplemented modules. Especially, we show that any finite direct sum of I-Rad-⊕-supplemented modules is I-Rad-⊕-supplemented. We also prove that an R-module M is I-Rad-⊕-supplemented if and only if K and MK ${M \over K}$ are I-Rad-⊕-supplemented for a fully invariant direct summand K of M. Finally, we determine the structure of I-Rad-⊕-supplemented modules over a discrete valuation ring.

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