Rings Whose Modules Have Grade Zero
Author: Wu, Zhi
Source: Acta Mathematica Sinica, Volume 21, Number 2, April 2005 , pp. 249-260(12)
Abstract:In this paper, we prove that R is a two-sided Artinian ring and J is a right annihilator ideal if and only if (i) for any nonzero right module, there is a nonzero linear map from it to a projective module; (ii) every submodule of R R is not a radical module for some right coherent rings. We call a ring a right X ring if Hom R (M, R) = 0 for any right module M implies that M = 0. We can prove some left Goldie and right X rings are right Artinian rings. Moreover we characterize semisimple rings by using X rings. A famous Faith’s conjecture is whether a semipimary PF ring is a QF ring. Similarly we study the relationship between X rings and QF and get many interesting results.
Document Type: Research Article
Affiliations: Email: firstname.lastname@example.org
Publication date: 2005-04-01