查询词典 finitely generated ideal

A group is '''finitely generated'''(respectively '''finitely related''','''finitely presented''') if it has a presentation that is finitely generated (respectively finitely related, a finite presentation).

群是'''有限生成'''的(分别为'''有限关联'''的，'''有限展现'''的)，如果它有有限生成的(分别为有限关联的，有限展示的)的展示。

Theorem 2.1.4 The following statements are equivalent for a ring R:(1) R is left co-semihereditary;(2) every finitely cogenerated factor module of a finitely cogenerated injective R-module is quasi-injective;(3) every finitely cogenerated factor module of a finitely cogenerated injective R-module is direct-injective.

an环 R下列叙述等价： l）R的每个商环是强左余半遗传的； 2）R的每个商环是左余半遗传的； 3）拟内射R模的每个有限余生成商模是拟内射的； 4）有限余生成拟内射R－模的每个有限余生成商是直内射的； 5）有限余生成fi－(来源：A3fBC论文网www.abclunwen.com)拟内射R－模的有限余生成商模是拟内射的。

Not every subgroup of a D-group is also a D-group. If a subgroup is a D-group we call the subgroup "sub- D -group." The "commutator ideal" of G is the smallest sub-D-group containing its commutator subgroup. We found that the commutator ideal can be viewed as a finitely generated module over a ring when G is a finitely generated metabelian D-group.

并非每个子群都是一个可除群，若一个子群是可除群，我们称之为子可除群(sub-D-group)，而G 的交换子理想则是在G中包含其导出群的最小子可除群，我们发现当G是一个有限生成亚交换可除群时，其交换子理想是一个有限生成模。

The first chapter, main instead " duo-ring " condition of " every maximal left ideal is GW-ideal " condition,study strongly regularities of GP-V-ring on this condition.lt is shown that (1) R is strongly regular iff R is left GP-V-ring whose maximal left ideals are GW-ideal.(2)R is strongly regular iff R is left GP-V-ring whose maximal right ideals are GW-ideal. The second chapter, generalize some results of GP-V-ring to GP-V-ring, discuss regularity of GP-V-ring.It is shown that (1) R is left self-injective regular with non-zero socle iff R is left GP-V -ring with Soc = Soc and R contains an injective maximal left ideal.(2)R is regular ring and every maximal essential left ideal is ideal iff R is left GP-injective left GP-V -ring and every maximal essential left ideal is ideal.

第一章主要将"duo-环"条件替换成"每一极大左理想是GW-理想"条件，研究在此条件下，GP-V-环的强正则性，证明了：(1)R是强正则环当且仅当R是左GP-V-环且R的每一极大左理想是广义弱理想；(2)R是强正则环当且仅当R是左GP-V-环且R的每一极大右理想是广义弱理想，第二章，主要将GP-V-环上一些结果推广到GP-V′-环上，讨论GP-V′-环的正则性，证明了：(1)R是左自内射正则环且Soc≠0当且仅当R是包含内射极大左理想的GP-V′-环，且Soc=Soc；(2)R是正则环且每一极大本质左理想是理想当且仅当R是左GP-内射的左GP-V′-环且每一极大本质左理想是理想。

A ring R is called right co-coherent if every finitely cogenerated factor module of a finitely cogenerated injective right R-module is finitely corelated.

如果有限余生成内射右R-模的有限余生成商模是有限余相关的，则R称为右余凝聚的。

In this paper,the nonstandard analysis theory is used for inducing a metric space by a Loeb measure space.On this basis,a metric space is induced by a internal finitely additive measure space.The close relationship between the metric space induced by a Loeb measure space and the metric space induced by a internal finitely additive measure space is illustrated with the concepts and some properties of Loeb measure.Then,some properties of the metric space that induced by a internal finitely additive measure space are studied.In the first two chapters,we first Succinctly present the origin,development and research states of the nonstandard analysis.Then,the theoretical foundation of nonstandard analysis as well as the axiomatic nonstandard analysis are given.Finally, the nonstandard model and the saturation model are discussed,as well as some natures of the nonstandard model and several equivalent conditions of saturation model are given.

本文利用非标准分析理论，在由Loeb测度空间导出度量空间的基础上，由内有限可加测度空间导出了度量空间，并借助Loeb测度的概念和若干性质证明了由标准的测度空间导出的度量空问和由内有限可加测度这个非标准的测度空间导出的度量空间有着密切的关系，在此关系的基础上还研究了由有限可加测度这个非标准的测度空间导出的度量空间的性质在第一、第二章里，我们首先简单介绍了非标准分析的产生、发展及研究现状，接着给出了非标准分析的理论基础以及公理化的非标准分析，进而讨论了非标准模型和饱和模型，并给出了非标准模型的一些性质和饱和模型的若干等价条件。

A ring R is called right co-semihereditary if every finitely cogenerated factor module of a finitely cogenerated injective right R-module is injective.

如果有限余生成内射右R-模的有限余生成商模是内射的，则R称为右余半遗传的。

Finally, after defining an evaluation module of the corresponding Loop superalgebra (Section 4), two major results of the paper -Theorem 4.land Theorem 4.2 are proved: Theorem 4.1 reduces the irreducibility of the tensor product of finitely many evaluation modules to the irreducibility of the tensor product of finitely many irreducible modules of a nilpotent Lie superalgebra; Theorem 4.2 gives a criterion for the tensor product of such modules to be irreducible.

第4节在定义了相应的Loop超代数的赋值模之后，证明了本文的两个主要结论：定理4.1和定理4.2。定理4.1将有限多个赋值模其张量积的不可约性归结为一幂零李超代数的限多个不可约模其张量积的不可约性；定理4.2利用不可约指标给出了一幂零李超代数的限多个不可约模其张量积仍不可约的判别准则。

According to the existence results of general equilibrium problems and vector equilibrium problems have been studied more and more. Inspired and motivated by these research results, this paper is devoted to study systematically a class of equilibrium problems, which is unify and extension of a large number of known equilibrium problems and variational inequalities problems. The research is carried on from three aspects.Firstly, in finitely continuous topological spaces, we introduce four new types of the system of generalized vector quasi-equilibrium problems, and we derive some existence results of a solution for the system of generalized vector quasi-equilibrium problems via the maximal element theorems in product finitely continuous topological spaces.Secondly, in complete metric spaces, we provide the Ekeland variational principle to equilibrium problems with set-valued maps. And via the Ekeland variational principle, existence results for vector equilibrium problem with set-valued maps and the system of vector equilibrium problem with set-valued maps.

针对一般的均衡问题和向量均衡问题解的存在性，已有许多研究成果，受这些成果的启发，本文主要从理论上较为系统地研究了一类均衡问题，它统一和推广了许多已有的均衡问题和变分不等式问题，研究分有三个方面；首先，在有限连续拓扑空间中，我们提出了四类广义向量拟均衡系，并借助于有限连续拓扑空间中的极大元定理讨论了这四类均衡系问题的解的存在性问题，然后，在完备度量空间中，我们给出了关于集值均衡问题的Ekeland变分原理，并利用Ekeland变分原理分别讨论了集值向量均衡问题和集值向量均衡系问题的解的存在性。

So we neglect that he was a practical esthetics in different degree. This paper tries to relocate his aesthetic ideal. Treating his as an aesthetician of aesthetic life, with the development clues of his aesthetic ideal of aesthetic life, ideal state and egos of practical esthetics. Then, analyzes how he combined aesthetic ideal and life ideal with life practice to realize his aesthetic and poetic life.

本文正是试图对他的美学思想做一个重新定位，把他视为一位审美人生美学家展开研究，以他的审美人生美学思想的发展为线索，通过对他的审美人生美学的理想范型、理想境界以及自我实践的研究，来看他是如何将美学思想与人生理想统一于人生实践，实现其审美化、诗意化的人生。

After explaining total design of automated test system for microcircuit , the thesis introduces GPIB standard .

文章在说明了微电路模块自动测试系统的总体设计后，对GPIB标准进行了介绍。

He interceded in my behalf.

他替我说情。