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环R称为N-环,如果R的素根N(R)={r∈R|存在自然数n使rn=0}.本文不仅对N-环进行了刻划,而且还研究了N-环的VonNeumann正则性.特别证明了:对于N-环R,如下条件是等价的:(1)R是强正则环;(2)R是正则环;(3)R是左SP-环;(4)R是右SF-环;(5)R是MELT,左p-V-环;(6)R是MERT,右p-V-环.因此推广了文献[4]中几乎所有的重要结果,同时也改进或推广了其它某些有关正则环的有用结果. 相似文献
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ERGODIC THEOREMS FOR LINEAR GROWTH PROCESSES WITH DIFFUSION 总被引:1,自引:0,他引:1
In this paper a simple class of the infinite dimensional reaction-diffusion processes——the linear growth processes with diffusion is studied. This paper is devoted to the ergodicity of these processes. Tne exact value of parameters at which the change of phase occurs is given, the set of all translation invariant invariant measures and the corresponding domain of attraction for each translation invariant invariant measure are described. 相似文献
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