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101.
《Journal of Pure and Applied Algebra》2023,227(2):107188
We present various approaches to J. Herzog's theory of generalized local cohomology and explore its main aspects, e.g., (non-)vanishing results as well as a general local duality theorem which extends, to a much broader class of rings, previous results by Herzog-Zamani and Suzuki. As an application, we establish a prescribed upper bound for the projective dimension of a module satisfying suitable cohomological conditions, and we derive some freeness criteria and questions of Auslander-Reiten type. Along the way, we prove a new characterization of Cohen-Macaulay modules which truly relies on generalized local cohomology, and in addition we introduce and study a generalization of the notion of canonical module. 相似文献
102.
《Journal of Pure and Applied Algebra》2023,227(6):107311
The present paper, though inspired by the use of tensor hierarchies in theoretical physics, establishes their mathematical credentials, especially as genetically related to Lie algebra crossed modules. Gauging procedures in supergravity rely on a pairing – the embedding tensor – between a Leibniz algebra and a Lie algebra. Two such algebras, together with their embedding tensor, form a triple called a Lie-Leibniz triple, of which Lie algebra crossed modules are particular cases. This paper is devoted to showing that any Lie-Leibniz triple induces a differential graded Lie algebra – its associated tensor hierarchy – whose restriction to the category of Lie algebra crossed modules is the canonical assignment associating to any Lie algebra crossed module its corresponding unique 2-term differential graded Lie algebra. This shows that Lie-Leibniz triples form natural generalizations of Lie algebra crossed modules and that their associated tensor hierarchies can be considered as some kind of ‘lie-ization’ of the former. We deem the present construction of such tensor hierarchies clearer and more straightforward than previous derivations. We stress that such a construction suggests the existence of further well-defined Leibniz gauge theories. 相似文献
103.
超声相控阵技术是目前聚乙烯管道热熔接头内部缺陷检测的一种主流方法。提出了基于注意力机制的改进Faster-RCNN目标检测网络用于超声相控阵D扫图聚乙烯管接头内部缺陷检测。针对聚乙烯管道热熔接头内部超声相控阵D扫图小缺陷较多、特征信息容易丢失的问题,将残差网络(ResNet50)与特征金字塔网络(FPN)相结合作为骨干网络,并引入卷积注意力模块(CBAM)自适应细化特征。将SSD网络框架和Faster-RCNN网络框架用于模型训练和测试,使用VGG16、ResNet50、ResNet50+FPN、ACBM+ResNet50+FPN作为骨干网络依次对超声相控阵聚乙烯管道热熔对接接头内部缺陷样本进行训练对比。结果表明,改进的Faster-RCNN网络模型在聚乙烯管接头内部缺陷检测和分类方面有明显改进,对小缺陷的检测性能有了显著的提高。 相似文献
104.
The main results of this paper are in two directions. First, the family of finite local Frobenius non-chain rings of length 4 (hence of nilpotency index 3) is determined. As a by-product all finite local Frobenius non-chain rings with elements, (p a prime) are given. Second, the number and structure of γ-constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3, of length relatively prime to the characteristic of the residue field of the ring, are determined. 相似文献
105.
Yeliz Kara 《代数通讯》2017,45(8):3627-3635
In this article, we focus on modules with the property that every projection invariant submodule is essential in a fully invariant direct summand. In contrast to π-extending condition, it is shown that the former property is inherited by direct summands and Morita invariant. An application of our results yields that the endomorphism ring of a free module enjoys the property. Moreover, we characterize generalized triangular matrix rings with the aforementioned property and apply to somewhat special cases. 相似文献
106.
107.
Abel群的一些分解定理的推广(I) 总被引:2,自引:2,他引:0
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. 相似文献
108.
Derya Keskı̇n Tütüncü 《代数通讯》2017,45(2):688-693
In this paper we provide conditions under which automorphism-coinvariant modules over a right perfect ring are quasi-projective. 相似文献
109.
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] where the normality is described in terms of the “shape” of the canonical module. 相似文献
110.