1) closed-dual module
闭偶模
1.
In this paper, we mainly investigate modules and rings with the property that closed submodules are annihilators, which are called closed-dual modules and closed-dual rings.
主要研究闭子模都是零化子的模与环,即闭偶模与闭偶环,刻画了闭偶模和闭偶环,给出了n阶矩阵环Mn(R)为闭偶环的一些等价条件,证明了环R是右非奇异右扩张环当且仅当R是右闭偶Baer环。
2) dual module
偶模
1.
Using R-dual modules we obtain an exact sequence of ExtnR(M,R) and show that for a coherent left perfect ring R,the finitely presented dimensions of ExtmR(M,R),m≥0 is less than that of M,which generalizes the corresponding result in[1].
利用R-偶模得到了ExtnR(M,R)的正合列,证明了在凝聚左完全环R下,ExtRm(M,R),(m≥0)的有限表示维数不超过M的有限表示维数,推广了文献[1]的结果。
2.
Using U-dual modules obtain an exact sequence of ExtnR(M,U),and show that for a right coherent ring R,or a coherent left perfect ring R,the flat dimensions,projective dimensions and finitely presented dimensions of ExtmR(M,U)(m≥0) are less than the corresponding dimensions of M.
设SUR为双模,给出了投射模的U-偶模为平坦模,投射模等特殊模的若干刻画,并利用U-偶模得到了关于Ex tnR(M,U)的正合列,从而证明了在右凝聚环、凝聚左完全环下,Ex tmR(M,U)(m≥0)的平坦维数、投射维数、有限表现维数等均不超过M的相应维数。
3) even illumination
偶模，偶数模
4) blocked-couplerTo whom correspondence should be addressed
封闭偶合剂
6) dual factor closed set
对偶因数封闭集
1.
Dual factor closed set is defined and the properties of GCD and LCM matrices defined on dual factor closed set and least common multiple cioed set are discussed.
给出了对偶因数封闭集的定义，讨论了对偶因数封闭集和最小公倍数封闭集上的矩阵（S）和［S］的性质。
补充资料：假中闭户终日偶得绝句
【诗文】：
官身常欠读书债，禄米不供沽酒资。
剩喜今朝寂无事，焚香闲看玉溪诗。
【注释】：
【出处】：
官身常欠读书债，禄米不供沽酒资。
剩喜今朝寂无事，焚香闲看玉溪诗。
【注释】：
【出处】：
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条