Pure Hereditary Rings
Pure Hereditary Rings
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DOI：
10.1080/00927870802272092
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发表时间：
2009-06
影响因子：
0.7
通讯作者：
Yuxian Geng;Nanqing Ding
中科院分区：
文献类型：
--
作者：
Yuxian Geng;Nanqing Ding
本文引入纯遗传环的概念，作为纯半单环和遗传环概念的非平凡推广。给出了纯遗传环的一些性质和例子。对于正整数n，设n是所有投射维数≤ n的左R-模的类。本文证明了左纯遗传环上有一个完全遗传余挠对，从而部分肯定地回答了Göbel和Trlifaj的一个问题.对类中的模块也进行了研究。特别注意n = 1的情况。
In this article, the notion of pure hereditary rings is introduced as a nontrivial generalization of the notion of both pure semisimple rings and of hereditary rings. Some properties and examples of pure hereditary rings are given. For a positive integer n, let 𝒫 n be the class of all left R-modules with projective dimension ≤ n. It is shown that over a left pure hereditary ring is a perfect and hereditary cotorsion pair, which gives a partial positive answer to a question of Göbel and Trlifaj. The modules in the class are also studied. Special attention is paid to the case n = 1.