共查询到20条相似文献,搜索用时 0 毫秒
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Reza Ebrahimi Atani 《代数通讯》2013,41(2):776-791
We classify all those indecomposable semiprime multiplication modules with finite-dimensional top over pullback of two Dedekind domains. We extend the definition and results given in [9] to a more general semiprime multiplication modules case. 相似文献
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We study injective hulls of simple modules over differential operator rings R[θ; d], providing necessary conditions under which these modules are locally Artinian. As a consequence, we characterize Ore extensions of S = K[x][θ; σ, d] for σ a K-linear automorphism and d a K-linear σ-derivation of K[x] such that injective hulls of simple S-modules are locally Artinian. 相似文献
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If M and N are right R-modules, M is called Socle-N-injective (Soc-N-injective) if every R-homomorphism from the socle of N into M extends to N. Equivalently, for every semisimple submodule K of N, any R-homomorphism f : K → M extends to N. In this article, we investigate the notion of soc-injectivity. 相似文献
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研究(?)Ri的由Ri(i=1,2,…,p)的序所诱导的序,证明(?)Ri在一定条件下作成一个有单位元的f环,并在有单位元的K-f环上的格序模范畴中引入保格R1(?)R2映射,进一步定义了张量积,使张量积概念在不同序环的序模范畴得到拓展. 相似文献
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SomeRingsCharacterizedbyModules¥YaoZhongping;WangDingguo(LiaochengTeacher'sCollege,Liaocheng252059)(QufuNormalUniveralty,Qufu... 相似文献
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We denote by 𝒜(R) the class of all Artinian R-modules and by 𝒩(R) the class of all Noetherian R-modules. It is shown that 𝒜(R) ? 𝒩(R) (𝒩(R) ? 𝒜(R)) if and only if 𝒜(R/P) ? 𝒩(R/P) (𝒩(R/P) ? 𝒜(R/P)), for all centrally prime ideals P (i.e., ab ∈ P, a or b in the center of R, then a ∈ P or b ∈ P). Equivalently, if and only if 𝒜(R/P) ? 𝒩(R/P) (𝒩(R/P) ? 𝒜(R/P)) for all normal prime ideals P of R (i.e., ab ∈ P, a, b normalize R, then a ∈ P or b ∈ P). We observe that finitely embedded modules and Artinian modules coincide over Noetherian duo rings. Consequently, 𝒜(R) ? 𝒩(R) implies that 𝒩(R) = 𝒜(R), where R is a duo ring. For a ring R, we prove that 𝒩(R) = 𝒜(R) if and only if the coincidence in the title occurs. Finally, if Q is the quotient field of a discrete valuation domain R, it is shown that Q is the only R-module which is both α-atomic and β-critical for some ordinals α,β ≥ 1 and in fact α = β = 1. 相似文献
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本文给出了Auslander-Gorenstein滤环上全律模(holonomicmodules)的一个特征簇刻划,由此得到了通过特征理想的极小素因子(有限个)计算余维数的公式。 相似文献
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本文给出了Auslander-Gorenstein滤环上全律模(holonomicmodules)的一个特征簇刻划,由此得到了通过特征理想的极小素因子(有限个)计算余维数的公式。 相似文献
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Prime Submodules and Flat Modules 总被引:2,自引:0,他引:2
A. AZIZI 《数学学报(英文版)》2007,23(1):147-152
In this paper, some characterizations of prime submodules in flat modules and, particularly, in free modules are given. Furthermore, the height of prime submodules and some saturated chain of prime submodules are also given. 相似文献
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Mohammad Ashraf Nadeem-ur-Rehman Shakir Ali 《Southeast Asian Bulletin of Mathematics》2002,25(3):379-382
Let R be a prime ring with characteristic different from two and U be a Lie ideal of R such that u2 U for all u U. In the present paper it is shown that if d is an additive mappings of R into itself satisfying d(u2) = 2ud(u), for all u U, then either U Z(R) or d(U) = (0).1991 Mathematics Subject Classification 16W25 16N60 相似文献
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Rachid Tribak 《代数通讯》2013,41(8):3190-3206
We introduce and study the notion of wd-Rickart modules (i.e. modules M such that for every nonzero endomorphism ? of M, the image of ? contains a nonzero direct summand of M). We show that the class of rings R for which every right R-module is wd-Rickart is exactly that of right semi-artinian right V-rings. We prove that a module M is dual Baer if and only if M is wd-Rickart and M has the strong summand sum property. Several structure results for some classes of wd-Rickart modules and dual Baer modules are provided. Some relevant counterexamples are indicated. 相似文献
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A module M is called extending if, for any submodule X of M, there exists a direct summand of M which contains X as an essential submodule, that is, for any submodule X of M, there exists a closure of X in M which is a direct summand of M. Dually, a module M is said to be lifting if, for any submodule X of M, there exists a direct summand of M which is a co-essential submodule of X, that is, for any submodule X of M, there exists a co-closure of X in M which is a direct summand of M. Okado (1984) has studied the decomposition of extending modules over right noetherian rings. He obtained the following: A ring R is right noetherian if and only if every extending R-module can be expressed as a direct sum of indecomposable (uniform) modules. In this article, we show that every (finitely generated) lifting module over a right perfect (semiperfect) ring can be expressed as a direct sum of indecomposable modules. And we consider some application of this result. 相似文献