Characterization of V-modules by Relative Quasi-continuity

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＬｅｔＲｂｅａｒｉｎｇｗｉｔｈｉｄｅｎｔｉｔｙａｎｄＭａｌｅｆｔＲ ｍｏｄｕｌｅ .ＡｌｅｆｔＲ ｍｏｄｕｌｅＵｉｓｃａｌｌｅｄＭ ｉｎｊｅｃｔｉｖｅｉｆ,ｆｏｒｅｖｅｒｙｓｕｂｍｏｄｕｌｅＮｏｆＭａｎｄｅｖｅｒｙｈｏｍｏｍｏｒｐｈｉｓｍ :Ｎ→Ｕ ,ｃａｎｂｅｅｘｔｅｎｄｅｄｔｏａｈｏｍｏｍｏｒｐｈｉｓｍ ψ :Ｍ→Ｕ .ＡｌｅｆｔＲ ｍｏｄｕｌｅＭｉｓｃａｌｌｅｄａＶ ｍｏｄｕｌｅｂｙＲａｍａｍｕｒｔｈｉ[1]ａｎｄＴｏｍｉｎａｇａ[2 ](ａｎｄｉｓｃａｌｌｅｄａｃｏ ｓｅｍｉｓ…     

高清医用电子内窥镜微型CMOS摄像模组

研发并报道一个全新的130万像素电子内窥镜微型摄像模组.该模组采用低压差分信号技术实现图像数据的长距离高保真传输,它包括一个1/5.5英寸、分辨率为1 280×1 024像素的CMOS图像传感器,一个视场角为140°的小型镜头以及2个电路板.小型镜头座直接粘合到图像传感器的非光学窗口部分,两块印刷电路板垂直装配,使模组的尺寸缩小到长宽高分别为15.0 mm、5.5 mm、5.2 mm的空间.编码芯片将并行数字信号编码成低压差分信号经双绞线传出模组.搭建了实验系统并对摄像模组的实践性能进行评价.实验表明:模组分辨率达到136 lp·mm-1,图像传输距离达到2 m以上.紧凑的结构、高清分辨率图像、大视场和长传输距离使其适用于内窥镜诊治,特别是高清胃镜和结肠镜.     

Rugged modules: The opposite of flatness

Relative notions of flatness are introduced as a mean to gauge the extent of the flatness of any given module. Every module is thus endowed with a flatness domain and, for every ring, the collection of flatness domains of all of its modules is a lattice with respect to class inclusion. This lattice, the flatness profile of the ring, allows us, in particular, to focus on modules which have a smallest flatness domain (namely, one consisting of all regular modules.) We establish that such modules exist over arbitrary rings and we call them Rugged Modules. Rings all of whose (cyclic) modules are rugged are shown to be precisely the von Neumann regular rings. We consider rings without a flatness middle class (i.e., rings for which modules must be either flat or rugged.) We obtain that, over a right Noetherian ring every left module is rugged or flat if and only if every right module is poor or injective if and only if R = S×T, where S is semisimple Artinian and T is either Morita equivalent to a right PCI-domain, or T is right Artinian whose Jacobson radical properly contains no nonzero ideals. Character modules serve to bridge results about flatness and injectivity profiles; in particular, connections between rugged and poor modules are explored. If R is a ring whose regular left modules are semisimple, then a right module M is rugged if and only if its character left module M⁺ is poor. Rugged Abelian groups are fully characterized and shown to coincide precisely with injectively poor and projectively poor Abelian groups. Also, in order to get a feel for the class of rugged modules over an arbitrary ring, we consider the homological ubiquity of rugged modules in the category of all modules in terms of the feasibility of rugged precovers and covers for arbitrary modules.     

强W-Gorenstein 复形

对自正交模类$\mathcal{W}$,引入了强$\mathcal{W}$-Gorenstein复形的概念.给出了强$\mathcal{W}$-Gorenstein复形的刻画,并将其应用到强Gorenstein内射复形.     

Gorenstein平坦模与Frobenius扩张

设R■A是环的Frobenius扩张,其中A是右凝聚环,M是任意左A-模.首先证明了_AM是Gorenstein平坦模当且仅当M作为左R-模也是Gorenstein平坦模.其次,证明了Nakayama和Tsuzuku关于平坦维数沿着Frobenius扩张的传递性定理的"Gorenstein版本":若_AM具有有限Gorenstein平坦维数,则Gfd_A(M)=Gfd_R(M).此外,证明了若R■S是可分Frobenius扩张,则任意A-模(不一定具有有限Gorenstein平坦维数),其Gorenstein平坦维数沿着该环扩张是不变的.     

形式三角矩阵环的Gorenstein遗传性和FP-内射性

我们研究了形式三角矩阵环上模的Gorenstein(半遗传)遗传性,有限表现性和FP-内射性.给出了形式三角矩阵环是Gorenstein(半遗传)遗传的充要条件,并得出了形式三角矩阵环是n-FC环的充分条件.     

Noether环的几点注记

本文利用特征模给出了Ｎｏｅｔｈｅｒ环的一些充分必要条件，并由此讨论了Ｎｏｅｔｈｅｒ环上的内射模与平坦模的一些性质     

Interval Valued Intuitionistic （S, T）-fuzzy Hv-submodules

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy Hv-submodules of an Hv-module with respect to a t-norm T and an s-norm S is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated. In particular, the connections between interval valued intuitionistic （S, T）-fuzzy Hv-submodules and interval valued intuitionistic （S, T）-fuzzy submodules are discussed.     

On the Decomposition of Hopf Module Coalgebra

In1969,Sweedler[1]giventhedecompositiontheoreyofcoalgebraswhicharecocommu-tative.In1975,Kaplansky[2]showedthatanycoalgebracanbeuniquelydecomposedintoadirectsumofitsindecomposablesubcoalgebras.From1978to1992,Shudo[3]andXu[4]consructuredtheindecomposabledirectsumcomponentsofacoalggebra,viadefineequivalenceralationforthesetofsimplesubcoalgebras.Asweknow,themodolecoalgebraisthennaturalgeneralizationofcoalgebra.AndittakesplayanimportentroleintheDrinfelddouble.Inthispaper,wediscussthedecompositio…