(3) For a ring R the following are equivalent:(i) R is n-regular rings(ii) R is right n-C2 rings and right n-Gpp rings.
证明了如下结果:(1)环R是n-C2环当且仅当n∈Z+,对于a∈R,若r(an)=r(e),其中e2=e∈R,则e∈Ran;(2)若R是右n-C2环,则Zr(R)J(R);(3)若R是一个环,则下列条件等价:(i)R是n-正则环;(ii)R是右n-C2环和右n-Gpp环。
In this paper,we mainly prove the followings are equivalent: (1) R is a n-regular ring; (2) Every left(right) R-module is Wnil-injective; (3) Every cyclic left(right) R-module is Wnil-injective; (4) R is a left(right) GNPP,left(right) Wnil-injective ring.
本文中,我们主要证明以下陈述等价:(1)R是n-正则环;(2)每一个左(右)R-模是Wnil-内射的;(3)每一个循环左(右)R-模是Wnil-内射环;(4)R是左(右)GNPP,左(右)Wnil-内射环。
Let G be a strong regular graph(denoted by srg in short) with parameters(n,k,λ,μ).
设G是一个具有参数(n,k,λ,μ)的强正则图,首先讨论了图G的一些性质以及参数n,k,λ和μ之间的关系,特别地,提出了一个关于参数n,k,λ和μ的整性条件。
On Coherent Rings,Hereditary Rings and Regular Rings;
Coherent环、fp_n-遗传环和fp_n-正则环
N-clean Rings,Semi-Regular Rings and Morita Contexts;
Morita Contexts与n-clean环和半-正则环
4-regular Simple Graph of Order n not Necessarily Contains 3-regular Subgraph of Order n;
n阶4正则简单图不一定含n阶3正则子图
Semigroup with Left Inside-Outside Law and Regular N(2,2,0) Algebras;
具有左里外律的半群与正则N(2,2,0)代数
Microcanonical statistics of R-N black holes with discrete spectrum
量子R-N黑洞系统的微正则系综统计
Assessment on Economic Benefit of N-1 Principle in Market Environment;
市场环境下N-1原则的经济效益评价
About Non-regular N-Spaces and Characterization of Metrizable Spaces in Terms of g-function;
关于非正则的N-空间及度量空间的g-函数刻画
A Logic System Based on Strong Regular Residuated Lattices and Its Completeness;
强正则剩余格值逻辑系统L~N及其完备性
On Von Neumann regularity of AGP-injective rings;
AGP—内射环的Von Neumann正则性
VON NEUMANN REGULARITY OF GP-V’-RINGS
GP-V'-环的von Neumann正则性
Morita Contexts Over Regular QB-rings
正则QB环上的Morita Contexts(英文)
Cotorsion envelopes of modules and VN-regular ring
模的Cotorsion包络与VN-正则环
N-semisimple rings,Noether N-semisimple rings and some special rings;
N-半单环、Noether N-半单环和几类特殊环
Necessary and sufficient conditions for the existence of globally stable positive equilibrium points of n-dimensional Lotka-Volterra circle systems
一类n维环型Lotka-Volterra系统正平衡点全局渐近稳定的充要条件(英文)
On YJ-Injective Modules and Characteristic Properties of Strongly Regular Rings;
关于YJ-内射模与强正则环的刻画
Von Neumamm Regularity in Terms of JGP-Injective
Von Neumann正则环的JGP-内射刻画
On Simple Singular YJ-injective Modules and Characterizations of Regular Rings
关于单奇异YJ-内射模与正则环的刻画
The relation between cyclic edge-connectivity and cyclic connectivity of 3-regular connected graphs
3-正则图的环边连通性和环连通性之间的关系