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On the Ding Injective Dimensions of Complexes 认领 引用
1
作者 Chiyu LONG Sixin ZHAO Bo LU 《Journal of Mathematical Research with Applications》 CSCD 2026年第2期175-196,共22页
In this paper,we study two types of the Ding injective dimensions of complexes.First,we provide some equivalent characterizations of the dimension related to the special Ding injec-tive preenvelopes.Furthermore,we con... In this paper,we study two types of the Ding injective dimensions of complexes.First,we provide some equivalent characterizations of the dimension related to the special Ding injec-tive preenvelopes.Furthermore,we consider the relationship between the dimensions Dipd(Y)and Did(Y)of the complex Y,where Dipd(Y)denotes the dimension associated with special Ding injective preenvelopes,and Did(Y)denotes the dimension associated with DG-injective resolutions.It is demonstrated that Dipd(Y)=Did(Y)for any bounded complex Y. 展开更多
关键词 Ding injective dimension special Ding injective preenvelope relative cohomology group
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Some Results of the Finitistic Injective Dimension of Rings 认领 引用
2
作者 XIONG Tao 《数学进展》 CSCD 北大核心 2026年第4期807-818,共12页
In this paper,we present some results of the finitistic injective dimension of pullbacks of rings in terms of strongly C2rings.
关键词 strongly C2ring pullback finitistic injective dimensior
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最大度至多为5的平面图的Injective边染色 认领 引用
3
作者 郭瑜倩 《应用数学进展》 2025年第11期22-29,共8页
图的injective边染色是指图中的任意两条距离为2的边或在同一个三角形的边不能染相同的颜色。称使得图具有injective边染色的最小正整数为图的injective边色数。本文运用权转移方法证明了以下结论:对于最大度小于等于5且无4-圈的平面图,... 图的injective边染色是指图中的任意两条距离为2的边或在同一个三角形的边不能染相同的颜色。称使得图具有injective边染色的最小正整数为图的injective边色数。本文运用权转移方法证明了以下结论:对于最大度小于等于5且无4-圈的平面图,其injective边色数小于等于21。 展开更多
关键词 Injective边染色 平面图 最大度 圈
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EXPLICIT DESCRIPTION OF A CLASS OF INDECOMPOSABLE INJECTIVE MODULES 认领 引用
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作者 M.R.Pournaki M.Tousi 《Acta Mathematica Scientia》 SCIE 2005年第3期511-514,共4页
Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p)≠0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module... Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p)≠0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module R/p. 展开更多
关键词 Noetherian ring injective module indecomposable injective module injective envelope weakly locally principal prime ideal
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On Pseudo Small Injective Modules 认领 引用
5
作者 ZHAO Yu, e DU Xian-neng 《Chinese Quarterly Journal of Mathematics》 CSCD 2013年第4期532-538,共7页
The definition of principally pseudo injectivity motivates us to generalize tae notion of injectivity, noted SP pseudo injectivity. The aim of this paper is to investigate characterizations and properties of SP pseudo... The definition of principally pseudo injectivity motivates us to generalize tae notion of injectivity, noted SP pseudo injectivity. The aim of this paper is to investigate characterizations and properties of SP pseudo injective modules. Various results are devel- oped, many extending known results. As applications, we give some characterizations on Noetherian rings, QI rings, quasi-Frobenius rings. 展开更多
关键词 SP pseudo injective modules semiregular modules SP injective modules co-Hopfian modules
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A Generalization of Gorenstein Injective and Flat Modules 认领 引用
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作者 LU BO Du Xian-kun 《Communications in Mathematical Research》 CSCD 2016年第4期339-351,共13页
In this article, we introduce and study the concept of n-Gorenstein injective （resp., n-Gorenstein flat） modules as a nontrivial generalization of Gorenstein injective （resp., Gorenstein flat） modules. We investig... In this article, we introduce and study the concept of n-Gorenstein injective （resp., n-Gorenstein flat） modules as a nontrivial generalization of Gorenstein injective （resp., Gorenstein flat） modules. We investigate the properties of these modules in various ways. For example, we show that the class of n-Gorenstein injective （resp., n -Gorenstein flat） modules is closed under direct sums and direct products for n ≥ 2. To this end, we first introduce and study the notions of n-injective modules and n-flat modules. 展开更多
关键词 n-injective module n-flat module n-Gorenstein injective module n- Gorenstein flat module preenvelope cover
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围长至少为5的平面图的injective-染色 认领 引用 被引量：3
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作者 卜月华 叶飘飘 《数学进展》 CSCD 北大核心 2018年第3期363-372,共10页
图G的injective k-染色是指映射c:V(G)→{1,2,…,k},使有公共邻点的两个顶点u,v满足c(u)≠c(v),用X_i(G)表示使G有一个injective k-染色的最小正整数k.对g(G)≥5的平面图G,若△(G)≥20,证明了X_i(G)≤△+3.
关键词 平面图 围长 injective染色 面
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On the Injective Equitable Domination of Graphs 认领 引用 被引量：1
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作者 Ahmad N. Alkenani Hanaa Alashwali Najat Muthana 《Applied Mathematics》 2016年第17期2132-2139,共8页
A dominating set D in a graph G is called an injective equitable dominating set (Inj-equitable dominating set) if for every , there exists such that u is adjacent to v and . The minimum cardinality of such a dominatin... A dominating set D in a graph G is called an injective equitable dominating set (Inj-equitable dominating set) if for every , there exists such that u is adjacent to v and . The minimum cardinality of such a dominating set is denoted by and is called the Inj-equitable domination number of G. In this paper, we introduce the injective equitable domination of a graph and study its relation with other domination parameters. The minimal injective equitable dominating set, the injective equitable independence number , and the injective equitable domatic number are defined. 展开更多
关键词 Domination Injective Equitable Domination Injective Equitable Domination Number
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围长至少为5的平面图的injective染色 认领 引用 被引量：1
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作者 卜月华 叶飘飘 《浙江师范大学学报（自然科学版）》 CAS 2017年第1期1-8,共8页
通过构造一个(Δ+3)-临界图G,运用权转移的方法证明了该图G不存在.同时,用反证法证明了:对于围长至少为5的平面图G,若Δ(G)≥30,则χi(G)≤Δ+3.这个结论改进了现有的一个结果.
关键词 平面图 围长 injective染色 面
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n-strongly Gorenstein Projective and Injective and Flat Modules 认领 引用 被引量：3
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作者 YANG Xiao-yan 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第4期553-564,共12页
In this paper, we study some properties of n-strongly Gorenstein projective,injective and flat modules, and discuss some connections between n-strongly Gorenstein injective, projective and flat modules. Some applicati... In this paper, we study some properties of n-strongly Gorenstein projective,injective and flat modules, and discuss some connections between n-strongly Gorenstein injective, projective and flat modules. Some applications are given. 展开更多
关键词 n-strongly Gorenstein projective module n-strongly Gorenstein injective module n-strongly Gorenstein flat module
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The Injective Chromatic Index of a Claw-Free Subcubic Graph is at Most 6 认领 引用
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作者 Xiaoyuan DONG Yuquan LIN Wensong LIN 《Journal of Mathematical Research with Applications》 CSCD 2023年第4期409-416,共8页
A coloring of edges of a graph G is injective if for any two distinct edges e1 and e2,the coloring of e1 and e2 are distinct if they are at distance 2 in G or in a common 3-cycle.The injective chromatic index of G is ... A coloring of edges of a graph G is injective if for any two distinct edges e1 and e2,the coloring of e1 and e2 are distinct if they are at distance 2 in G or in a common 3-cycle.The injective chromatic index of G is the minimum number of colors needed for an injective edge coloring of G.It was conjectured that the injective chromatic index of any subcubic graph is at most 6.In this paper,we partially confirm this conjecture by showing that the injective chromatic index of any claw-free subcubic graph is less than or equal to 6.The bound 6 is tight and our proof implies a linear-time algorithm for finding an injective edge coloring using at most 6 colors for such graphs. 展开更多
关键词 injective edge coloring injective chromatic index claw-free subcubic graph
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围长至少为5的平面图的injective列表染色 认领 引用 被引量：1
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作者 卜月华 王超 《浙江师范大学学报（自然科学版）》 CAS 2016年第1期6-12,共7页
研究了围长至少为5的平面图的injective列表染色问题.通过分析极小反例的结构性质并利用权转移方法,证明了围长至少为5且最大度至少为12的平面图G的injective列表色数不超过Δ(G)+4.此结果进一步拓展了平面图关于injective色数的Luar... 研究了围长至少为5的平面图的injective列表染色问题.通过分析极小反例的结构性质并利用权转移方法,证明了围长至少为5且最大度至少为12的平面图G的injective列表色数不超过Δ(G)+4.此结果进一步拓展了平面图关于injective色数的Luar猜想成立的充分条件. 展开更多
关键词 平面图 围长 injective列表染色 面
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Injective Envelopes of a Hilbert C~*Module 认领 引用
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作者 许天周 蔡涛 李炳照 《Journal of Beijing Institute of Technology》 EI CAS 2001年第2期119-124,共6页
As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelopes of... As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelopes of an extension of a Hilbert C * modules over a C * algebra is introduced, and is characterized in terms of the injectivity and essence. It is shown that every Hilbert C * module has a unique (up to H isometrics) injective envelope if it exists. It is also shown that an extension of a Hilbert C * module is an injective envelope if and only if it is an injective and essential extension. Moreover, every Hilbert C * module over a W * algebra has a unique (up to H isometrics) injective envelope and the injective envelope of a Hilbert C * module H is maximal essential extension of H . 展开更多
关键词 C * algebra Hilbert C * module injective envelope
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On Injective Lattice Implication Algebras 认领 引用
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作者 SONG Zhen-ming ZHENG Feng-bin 《Chinese Quarterly Journal of Mathematics》 2000年第1期65-70,共6页
Many-valued logic system always plays a crucial role in artificial intelligence.In orderfurther to study many-valued logic system as well as logic with truth-values in a lattice,the con-cept of lattice implication alg... Many-valued logic system always plays a crucial role in artificial intelligence.In orderfurther to study many-valued logic system as well as logic with truth-values in a lattice,the con-cept of lattice implication algebra was proposed in reference[1]and the corresponding logic systemwas also investigated.In this paper.we focus on a kind of important lattice implication algebra,i.e..injective lattice implication algebra.Some properties are discussed and also the charaeteristic ofits structure is given. 展开更多
关键词 lattice-valued logic system lattice implication algebras injective lattice implication alge-bras
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INJECTIVE MAPS ON PRIMITIVE SEQUENCES OVER Z/(p^e) 认领 引用
15
作者 Sun Zhonghua Qi Wenfeng 《Applied Mathematics(A Journal of Chinese Universities)》 2007年第4期469-477,共9页
Let Z/（p^e） be the integer residue ring modulo p^e with p an odd prime and integer e ≥ 3. For a sequence a over Z/（p^e）, there is a unique p-adic decomposition a- = a-0 ＋a-1 .p ＋… ＋ a-e-l .p^e-1 where each a-... Let Z/（p^e） be the integer residue ring modulo p^e with p an odd prime and integer e ≥ 3. For a sequence a over Z/（p^e）, there is a unique p-adic decomposition a- = a-0 ＋a-1 .p ＋… ＋ a-e-l .p^e-1 where each a-i can be regarded as a sequence over Z/（p）, 0 ≤ i ≤ e - 1. Let f（x） be a primitive polynomial over Z/（p^e） and G＇（f（x）,p^e） the set of all primitive sequences generated by f（x） over Z/（p^e）. For μ（x） ∈ Z/（p）[x] with deg（μ（x）） ≥ 2 and gad（1 ＋ deg（μ（x））,p- 1） = 1, setφe-1 （x0, x1,… , xe-1） = xe-1. [μ（xe-2） ＋ ηe-3（x0, X1,…, xe-3）] ＋ ηe-2（x0, X1,…, xe-2） which is a function of e variables over Z/（p）. Then the compressing mapφe-1 ： G＇（f（x）,p^e） → （Z/（p））^∞ ,a-→φe-1（a-0,a-1, … ,a-e-1） is injective. That is, for a-,b-∈ G＇（f（x）,p^e）, a- = b- if and only if φe-1 （a-0,a-1, … ,a-e-1） = φe-1（b-0, b-1,… ,b-e-1）. As for the case of e = 2, similar result is also given. Furthermore, if functions φe-1 and ψe-1 over Z/（p） are both of the above form and satisfy φe-1（a-0,a-1,…,a-e-1）=ψe-1（b-0, b-1,… ,b-e-1） for a-,b-∈G＇（f（x）,p^e）, the relations between a- and b-, φe-1 and ψe-1 are discussed 展开更多
关键词 integer residue ring linear recurring sequence primitive sequence injective map.
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Notes on Strongly n-Gorenstein Projective, Injective and Flat Modules 认领 引用 被引量：1
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作者 SHANG Wen-liang 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第3期389-396,共8页
In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, poly... In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, polynomial extensions and localizations. 展开更多
关键词 excellent extensions strongly n-Gorenstein projective modules strongly nGorenstein injective modules strongly n-Gorenstein flat modules
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Partitioning of Any Infinite Set with the Aid of Non-Surjective Injective Maps and the Study of a Remarkable Semigroup 认领 引用
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作者 Charif Harrafa 《Open Journal of Discrete Mathematics》 2020年第3期74-88,共15页
In this article, we will present a particularly remarkable partitioning method of any infinite set with the aid of non-surjective injective maps. The non-surjective injective maps from an infinite set to itself consti... In this article, we will present a particularly remarkable partitioning method of any infinite set with the aid of non-surjective injective maps. The non-surjective injective maps from an infinite set to itself constitute a semigroup for the law of composition bundled with certain properties allowing us to prove the existence of remarkable elements. Not to mention a compatible equivalence relation that allows transferring the said law to the quotient set, which can be provided with a lattice structure. Finally, we will present the concept of Co-injectivity and some of its properties. 展开更多
关键词 Partitioning Non-Surjective Injective Infinite Set Fixed Points Lattice Structure
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Complexity of Injective Homomorphisms to Small Tournaments, and of Injective Oriented Colourings 认领 引用
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作者 Russell J. Campbell Nancy E. Clarke Gary MacGillivray 《Open Journal of Discrete Mathematics》 2023年第1期1-15,共15页
Several possible definitions of local injectivity for a homomorphism of an oriented graph G to an oriented graph H are considered. In each case, we determine the complexity of deciding whether there exists such a homo... Several possible definitions of local injectivity for a homomorphism of an oriented graph G to an oriented graph H are considered. In each case, we determine the complexity of deciding whether there exists such a homomorphism when G is given and H is a fixed tournament on three or fewer vertices. Each possible definition leads to a locally-injective oriented colouring problem. A dichotomy theorem is proved in each case. 展开更多
关键词 Injective Graph Homomorphism Oriented Colouring Complexity
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SEEMINGLY INJECTIVE VON NEUMANN ALGEBRAS 认领 引用
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作者 Gilles PISIER 《Acta Mathematica Scientia》 SCIE CSCD 2021年第6期2055-2085,共31页
We show that a QWEP von Neumann algebra has the weak* positive approximation property if and only if it is seemingly injective in the following sense: there is a factorization of the identity of IdM= vu : M→uB(H)... We show that a QWEP von Neumann algebra has the weak* positive approximation property if and only if it is seemingly injective in the following sense: there is a factorization of the identity of IdM= vu : M→uB(H)→vM with u normal, unital, positive and v completely contractive. As a corollary, if M has a separable predual, M is isomorphic(as a Banach space) to B(l2). For instance this applies(rather surprisingly) to the von Neumann algebra of any free group. Nevertheless, since B(H) fails the approximation property(due to Szankowski) there are M ’s(namely B(H)** and certain finite examples defined using ultraproducts) that are not seemingly injective.Moreover, for M to be seemingly injective it suffices to have the above factorization of I dM through B(H) with u, v positive(and u still normal). 展开更多
关键词 von Neumann algebra injectivity positive approximation property
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A Note on DG-Gorenstein Injective Complexes 认领 引用 被引量：4
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作者 Bo Lu Kaiyang Lan 《Algebra Colloquium》 SCIE CSCD 2020年第4期731-740,共10页
The notion of DG-Gorenstein injective complexes is studied in this article.It is shown that a complex G is DG-Gorenstein injective if and only if G is exact with Zn(G)Gorenstein injective in R-Mod for each n∈Zand ... The notion of DG-Gorenstein injective complexes is studied in this article.It is shown that a complex G is DG-Gorenstein injective if and only if G is exact with Zn(G)Gorenstein injective in R-Mod for each n∈Zand any morphism f:E→G is null homotopic whenever E is a DG-injective complex. 展开更多
关键词 Gorenstein injective module DG-injective complex DG-Gorenstein injective complex
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