Abel群的一些分解定理的推广(I)

这项研究的目的是要把Abel群（有限或无限）的诸多分解定理尽可能地推广到主理想整环的模上,得到这类模上的分解定理,随后再把所得定理应用到向量空间（有限维或无限维）及其线性变换,得到向量空间的分解定理.本文是系列文章的第一篇,主要目的是建立起支撑整个研究的最基本概念,例如纯子模、有界模、局部循环模、具有minimax条件的模等.本文主要内容有： （1）确定了主理想整环上可除模、有界模、局部循环模的结构; （2）给出了主理想整环上拟循环模的生成性质,这类模在以后的研究里起着非常重要的作用; （3）描述了主理想整环上满足极小条件,minimax条件的模的结构; （4）给出了两个不同构的Z[i]-模,它们作为Abel群是同构的.     

Acetic acid permeation through photovoltaic backsheets: Influence of the composition on the permeation rate

Acetic acid, which is formed during degradation of the most frequently used photovoltaic (PV) encapsulant ethylene vinyl acetate (EVA), is linked to several PV module failure mechanisms like corrosion of interconnectors, cells or potential induced degradation (PID). An evaluation of a new measurement technique and data analysis for acetic acid permeation through photovoltaic backsheet films is described. The influence of the layer composition of the multilayer backsheets on the acetic acid permeation rates (AATR) was determined by investigating the permeation properties of the individual layers as well as the whole polymeric multilayer composites. Various polymeric backsheet types based on PET-core layers showing a very high barrier for acetic acid permeation were compared to fully polyamide material stacks which allow for a much higher transmission of acetic acid through the backsheet out of the module. Incorporated Al-layers were found to not affect the AATRs of PET based backsheets.     

A canonical module characterization of Serre’s (R1)

In this short note, we give a characterization of domains satisfying Serre’s condition (R₁) in terms of their canonical modules. In the special case of toric rings, this generalizes a result of the second author [9 Yanagawa, K. (2015). Dualizing complexes of seminormal a?ne semigroup rings and toric face rings. J. Algebra 425:367–391.[Crossref], [Web of Science ®] , [Google Scholar]] where the normality is described in terms of the “shape” of the canonical module.     

When automorphism-coinvariant modules are quasi-projective

In this paper we provide conditions under which automorphism-coinvariant modules over a right perfect ring are quasi-projective.     

Gorenstein injective envelopes and covers over two sided noetherian rings

We prove that the class of Gorenstein injective modules is both enveloping and covering over a two sided noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat. In the second part of the paper we consider the connection between the Gorenstein injective modules and the strongly cotorsion modules. We prove that when the ring R is commutative noetherian of finite Krull dimension, the class of Gorenstein injective modules coincides with that of strongly cotorsion modules if and only if the ring R is in fact Gorenstein.