NJ模与强NJ模

NJ MODULE AND STRONGLY NJ MODULE

本文用两种不同的方法将Nicholson定义的NJ环引入到模类中,给出NJ模和强NJ模的概念,证明了强NJ模一定是NJ模,给出了是NJ模但不是强NJ模的例子,并证明了两者在局部投射的情形下是等价的.文章还给出了NJ模和强NJ模一些重要的等价刻画,证明了在有限生成的条件下NJ模及强NJ模均为一些循环模的直和,且强NJ模一定是投射模.

The object of this paper is to lead the conception of NJ ring into module class with two methods,define NJ module and strongly NJ module. We prove that a strongly NJ module must be a NJ module; give example to show that a NJ module need not be a strongly NJ module; prove that in locally projective case the two are equivalent. We also give some important characterizations of the two module classes. It is show that under finite generated conditions both NJ modules and strongly NJ modules are direct sum of some cyclic modules, and strongly NJ modules are projective.