关于有正则元环的交换性定理

为了研究环的交换性条件,依据Herstein关于交换性的著名结论以及Jacobson密度定理等理论,讨论有中心正则元的环,在一定条件下的交换性,推广了一系列已有定理,该结论中多项式条件比较宽松,涵盖了多个已有结论.     

半质环的交换性条件

给出了Ｂａｅｒ半单纯环的两个交换性条件，并对其中心元进行了讨论，得到了两个结果。     

半质环的一个交换性结果

本文证明了半质环的一个交换性结果，推广了文献［３］～［２１］中的相关结果。     

Ω-代数遗传性的注记

探讨了Ω-代数的遗传性,即考察Ω-代数的生成元集的性质对Ω-代数自身性质的影响.证明了在一定条件下Ω-代数的交换性及从一个Ω-代数到另一个Ω-代数的同态映射都由Ω-代数的生成元集决定.     

半质环交换性的一个定理

给出了利用半质环满足多项式的某些系数和判别半质环为交换环的两个简易方法。     

Block checker/diagonal transformation matrices,their properties,and the interplay with fast-lifting

This article introduces what we call block checker matrices with some specific structures characterised by a set of integers, and then introduces the permutation matrices called block checker/diagonal (BCD) transformation matrices that relate block checker matrices with block diagonal matrices through similarity transformations. The study is motivated by the importance of the fast-lifting technique in control theory, especially in the study of sampled-data systems and time-delay systems. More precisely, it is partly motivated by the desire for alleviating the bother of describing the class of the matrices commuting with block diagonal matrices, and for such a purpose the permutation with BCD transformation matrices is helpful. The study further extends to investigating the various useful properties among BCD transformation matrices, as well as their interplay relations with various variants of fast-lifting, e.g. full-vector fast-lifting and subvector-wise fast-lifting, or one-stage fast-lifting and two-stage fast-lifting. The usefulness of the results in the context of the fast-lifting treatment is also suggested.     

半质环的交换性定理

证明了半质环的两个交换性定理,是满足可变恒等式的交换条件已知结果的推广。     

半质环的交换性条件

证明了满足下列条件的半质环是交换环:对R中任意元x,y存在整数s=s(x)>1,t=t(x)>1(或s=s(y)>1,t=t(y)>1),使得[xy,xxyy]∈Z(R).     

Jacobson半单纯环的几个交换性定理

本文利用线性稠密性定理,结合多项式条件,推广了郭元春,于东,卢玉贞的结论,给出并证明了Jacobson半单纯环的两个交换性定理.     

半质环的几个交换性定理

研究了半质环的交换性,给出了半质环的4个交换性条件,推广了郭元春的一些结果.