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11.
Paolo Zanardo 《代数通讯》2015,43(1):158-173
Let R be a commutative ring and A be an R-module. The Mal'cev rank μ(A) of A is the sup of genN, where N ranges over the finitely generated submodules of A, and genN is the minimum number of generators of N. We prove that μ is both sub-additive and pre-additive as an invariant of Mod(R). Our main goal is to investigate μ for modules over pseudo-valuation domains. Specifically, we establish which pseudo-valuation domains R satisfy the property that an R-module of finite Mal'cev rank must be finitely generated. We split the class 𝒞 of pseudo-valuation domains as a union 𝒞 = 𝒞1 ∪ 𝒞2 ∪ 𝒞3 ∪ 𝒞4 of suitably defined subclasses, and prove that the property holds if and only if R ∈ 𝒞3 ∪ 𝒞4. In that case we can describe the R-modules A where μ(A) < ∞. We also show that, for R ∈ 𝒞4, there exist indecomposable R-modules of arbitrarily large finite Mal'cev rank. 相似文献
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An experimental investigation is carried out to characterize the performance of thermoelectric modules used for electric power generation over a range of different resistance loads. The performance of a Peltier cell used as a thermoelectric generator is evaluated in terms of power output and conversion efficiency. The results show that a thermoelectric module is a promising device for waste heat recovery. 相似文献
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Strongly Gorenstein Flat Modules and Dimensions 总被引:1,自引:0,他引:1
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通过引用P-平坦模的定义,引入了右IPF环的概念,推广了右IF环的概念,这对研究IF环及QF环具有重要的作用,同时对右IPF环的性质作了一些刻画,得到了右IPF环的若干个等价命题;最后,用P-平坦模及右IPF环推出了正则环的一些等价条件. 相似文献
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Let A be a noetherian commutative Z[1/2]-algebra of Krull dimension d and let P be a projective A-module of rank d. We use derived Grothendieck-Witt groups and Euler classes to detect some obstructions for P to split off a free factor of rank one. If d?3, we show that the vanishing of its Euler class in the corresponding Grothendieck-Witt group is a necessary and sufficient condition for P to have a free factor of rank one. If d is odd, we also get some results in that direction. If A is regular, we show that the Chow-Witt groups defined by Morel and Barge appear naturally as some homology groups of a Gersten-type complex in Grothendieck-Witt theory. From this, we deduce that if d=3 then the vanishing of the Euler class of P in the corresponding Chow-Witt group is a necessary and sufficient condition for P to have a free factor of rank one. 相似文献
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提出了强拟Armendariz环的概念,给出了强Armendariz环和强拟Armendariz环上的一些结果. 相似文献
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An associative ring with identity R is called Armendariz if, whenever (∑^m i=0^aix^i)(∑^n j=0^bjx^j)=0 in R[x],aibj=0 for all i and j. An associative ring with identity is called reduced if it has no non-zero nilpotent elements. In this paper, we define a general reduced ring (with or without identity) and a general Armendariz ring (with or without identity), and identify a class of maximal general Armendariz subrings of matrix rings over general reduced rings. 相似文献