ω-Gorenstein injective modules and dimensions

Gorenstein injective modules and dimensions have been studied extensively by many authors. In this paper, we investigate Gorenstein injective modules and dimensions relative to a Wakamatsu tilting module.

Notes on Strongly n-Gorenstein Projective, Injective and Flat Modules

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.

On minimal quasi-injective modules and strong Kasch modules

设R为一个环，M为一个右R-模．若每个从M的单子模到M的同态都可以开拓为M的自同态，则称M为一个极小拟内射模．若每个单的右R-模都可以嵌入M，则称M为一个强Kasch模．本文研究了这两类模的一些刻画和性质．

n-strongly Gorenstein Projective and Injective and Flat Modules

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.

Some Studies on Quasi AP-injective Modules

Let R be a ring. R is called right AP-injective if, for any a E R, there exists a left ideal of R such that lr（a） = Ra＋Xa. We extend this notion to modules. A right R-module M with S = End（MR） is called quasi AP-injective if, for any s∈S, there exists a left ideal Xs of S such that ls（Ker（s）） = Ss＋Xs. In this paper, we give some characterizations and properties of quasi AP-injective modules which generalize results of Page and Zhou.

EXPLICIT DESCRIPTION OF A CLASS OF INDECOMPOSABLE INJECTIVE MODULES

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.

A Generalization of Gorenstein Injective and Flat Modules

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.

On Pseudo Small Injective Modules

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.

<i>S</i>-Injective Modules and Rings

We introduce and investigate the concept of s-injective modules and strongly s-injective modules. New characterizations of SI-rings, GV-rings and pseudo-Frobenius rings are given in terms of s-injectivity of their modules.

PS-injective Modules, PS-flat Modules and PS-coherent Rings

A left ideal I of a ring R is small in case for every proper left ideal K of R, K ＋ I ≠R. A ring R is called left PS-coherent if every principally small left ideal Ra is finitely presented. We develop, in this paper, PS-coherent rings as a generalization of P-coherent rings and J-coherent rings. To characterize PS-coherent rings, we first introduce PS-injective and PS-flat modules, and discuss the relation between them over some spacial rings. Some properties of left PS-coherent rings are also studied.

Some Notes on Quasi AP-injective Modules

Let R be a ring. A right R-module M with S = End（MR） is called a quasi AP-injective module, if, for any s C S, there exists a left ideal Xs of S such that ls（ker s） = Ss＋Xs. Let M be a quasi AP-injective module which is a self-generator. We show that for such a module, if S is semiprime, then every maximal kernel of S is a direct summand of M. Furthermore, if ker（a1） lohtain in ker（a2a1） lohtain in ker（a3a2a1） lohtain in... satisfy the ascending conditions for any sequence al, a2, a3,… ∈ S, then S is right perfect. In this paper, we give a series of results which extend and generalize results on AP-injective rings.

Injective Envelopes of a Hilbert C~*Module

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 .

A Pulse Width Modulation Scheme With Zero-sequence Voltage Injection for Single Phase Three-level NPC Rectifiers

直流侧中点电位电压偏移是多电平中性点钳位型变流器的主要缺点。以单相三电平NPC整流器为研究对象，以实现直流侧中点电位无漂移为控制目标，以传统的单相三电平单极性载波脉宽调制方法为基础，首先提出一种基于零序电压分量注入的载波脉宽调制算法；然后在此基础上给出基于零序电压分量极限值注入的载波脉宽调制算法；并给出这2种方法的零序电压分量的设计方案；最后，对这2种方法进行了详细的理论分析、计算机仿真和1kW样机实验对比验证。研究结果表明：所提出的2种算法都能有效实现直流侧中点电位平衡控制，其中基于零序电压分量极限值注入的载波调制算法的中点电位控制具有更快动态响应速度，且其网侧电流的高次谐波主要分布在开关频率附近；而基于零序电压分量注入的载波调制算法的网侧电流高次谐波主要分布在2倍开关频率附近。但是在一个调制信号周期内，基于零序电压分量极限值注入的载波调制算法的开关切换次数比基于零序电压分量注入的载波调制算法低25％左右。

Injection modulation of p^+-n emitter junction in 4H-SiC light triggered thyristor by double-deck thin n-base

To overcome hole-injection limitation of p^＋-n emitter junction in 4H-SiC light triggered thyristor, a novel high- voltage 4H-SiC light triggered thyristor with double-deck thin n-base structure is proposed and demonstrated by two- dimensional numerical simulations. In this new structure, the conventional thin n-base is split to double-deck. The hole- injection of p^＋-n emitter junction is modulated by modulating the doping concentration and thickness of upper-deck thin n- base. With double-deck thin n-base, the current gain coefficient of the top pnp transistor in 4H-SiC light triggered thyristor is enhanced. As a result, the triggering light intensity and the turn-on delay time of 4H-SiC light triggered thyristor are both reduced. The simulation results show that the proposed 10-kV 4H-SiC light triggered thyristor is able to be triggered on by 500-mW/cm^2 ultraviolet light pulse. Meanwhile, the turn-on delay time of the proposed thyristor is reduced to 337 ns.

Monolithic integration of electroabsorption modulators and tunnel injection distributed feedback lasers using quantum well intermixing

Electroabsorption modulators combining Franz-Keldysh effect and quantum confined Stark effect have been mono-lithically integrated with tunnel-injection quantum-well distributed feedback lasers using a quantum well intermixing method. Superior characteristics such as extinction ratio and temperature insensitivity have been demonstrated at wide temperature ranges.

Development of an injection-seeded single-frequency laser by using the phase modulated technique

An injection-seeded single-frequency Q-switched Nd：YAG laser is accomplished by using a phase modulated rampfire technique. A RbTiOPO4（RTP） electro-optic crystal is selected for effective optical path length modulation of the slave self-filtering unstable resonator. This single-frequency laser is capable of producing 50 m J pulse energy at 1 Hz repetition rate with a pulse width of 16 ns. The standard deviation of laser pulse intensity for consecutive 100 shots from the mean pulse intensity is less than 1.05%. A spectral linewidth of less than 0.5 pm with a frequency jitter of about 14 fm over30 min is obtained.

Some Equivalences and Dualities via Static Modules

For a ring A, an extension ring B, a fixed right A-module M, the endomorphism ring D formed by M, the endomorphism ring E formed by , and the endomorphism ring F formed by HomA (B,M), we present equivalences and dualities between subcategories of B-modules which are finitely cogenerated injective as A-modules and E-modules and F-modules which are finitely generated projective as D-modules.

IFP-FLAT DIMENSIONS AND IFP-INJECTIVE DIMENSIONS

In basic homological algebra, the flat and injective dimensions of modules play an important and fundamental role. In this paper, the closely related IFP-flat and IFP-injective dimensions are introduced and studied. We show that IFP-fd（M） = IFP-id（M＋） and IFP-fd（M＋）=IFP-id（M） for any R-module M over any ring R. Let ：Z-In （resp., ＂Zgv,~） he the class of all left （resp., right） R-modules of IFP-injective （resp., IFP-flat） dimension at most n. We prove that every right R-module has an IFn- preenvelope, （IFn,IF⊥n） is a perfect cotorsion theory over any ring R, and for any ring R with IFP-id（RR） 〈 n, （IIn,II⊥n） is a perfect cotorsion theory. This generalizes and improves the earlier work （J. Algebra 242 （2001）, 447-459）. Finally, some applications are given.

The embedded design verification test of microwave circuit modules based on specific chips

In the Paper,the author introduces an embedded design verification test based on specific chips to solve the technical problems of microwave circuit test and fault diagnosis.The author explains embedded design of microwave circuit modules and approach of hardware design and software design,and finally verifies the embedded design of microwave circuit modules based on specific chips.

Injective Cogenerators,Cotilting Modules and Cosilting Modules

It is well known that the concept of cotilting modules generalizes injective cogenerators and in turn,the concept of cosilting modules generalizes cotilting modules.In this paper,we further investigate the close connections among injective cogenerators,cotilting modules and cosilting modules from the viewpoint of morphism categories.Some applications are also given.