On networks over finite rings

doi:10.1016/j.jfranklin.2022.07.039

CSpace

	On networks over finite rings
	Cheng, Daizhan 1,2; Ji, Zhengping 1,3
	2022-09-01
发表期刊	JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
ISSN	0016-0032
卷号	359 期号:14 页码:7562-7599
摘要	The (control) networks over finite rings are proposed and their properties are investigated. Based on semi-tensor product (STP) of matrices, a set of algebraic equations are provided to verify whether a finite set with two binary operators is a ring. As an application, all rings with 4 elements are obtained. It is then shown that the STP-based technique developed for logical (control) networks are applicable to (control) networks over finite rings. A (control) sub-network over a proper ideal of the bearing ring is constructed. Certain properties are revealed, showing that a network over the ideal behaves like a subsystem over an invariant subspace. Product rings are then introduced, which provides a tool for both constructing product networks and decomposing complex networks. Finally, the representation of networks over finite rings is considered, which investigates how many finite networks can be expressed as networks over finite rings, showing that the technique developed in this paper is widely applicable. (C) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
DOI	10.1016/j.jfranklin.2022.07.039
收录类别	SCI
语种	英语
资助项目	NNSF[62073315] ; NNSF[61074114] ; NNSF[61273013]
WOS研究方向	Automation & Control Systems ; Engineering ; Mathematics
WOS类目	Automation & Control Systems ; Engineering, Multidisciplinary ; Engineering, Electrical & Electronic ; Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000855295200015
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61023
专题	中国科学院数学与系统科学研究院
通讯作者	Cheng, Daizhan
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 2.Liaocheng Univ, Res Ctr Semitensor Prod Matrices, Lianocheng, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Cheng, Daizhan,Ji, Zhengping. On networks over finite rings[J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS,2022,359(14):7562-7599.
APA	Cheng, Daizhan,&Ji, Zhengping.(2022).On networks over finite rings.JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS,359(14),7562-7599.
MLA	Cheng, Daizhan,et al."On networks over finite rings".JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 359.14(2022):7562-7599.