关于特殊根类格的原子的一个注记

A Note on the Atoms of the Lattice of Special Radical Classes

在本文中,我们对一类环给出一个定义,它是素单环和Halina的(*)一环的一个推广,部分地对偶于Barry的ACC-内射环。这样一个环能够生成持殊根类格的一个原子。这也和Halina〔2〕一样对Puezylowski和Poszkowska提出的问题〔1〕给出一个肯定的回答。但是,不幸的作者不能够构造或找到这样一个环R使得χ_r和H_r不含有素单环和(-)一环,其中K_r和H_r分别是包含R的最小特殊类和(R)的同态闭包。

In this paper, we give a definition for a kind of rings, which are generalizations of prime simple rings and Halina＇s (*)-rings, and partially dual to Barry＇s ACC-injective rings. Such a ring can generate an atom of the lattice of special radical classes. This also gives a posi- tive answer to Puczylowski＇s and Roszkowska＇s question like Halina But unfortunate- ly, the author is unable to build or find such a ring R that π_R and H_R contain no prime simple rings and (*)-rings, where π_R and H_R are, resp., the smallest special class containing R and the homomorphic closure of {R}.