四川师范大学学报（自然科学版）2013，Vol.36Issue(4)：500-503,4.DOI:10.3969/j.issn.1001-8395.2013.04.003
P-投射模的刻画
The Properties of P-Projective Modules
摘要
Abstract
A module M is called P-projective,if for any cyclic submodule Rx of any module N,every homomorphismf:M-N/Rx can be extended to a homomorphism g:M→N.In this paper,the new equivalent definitions of the P-projective module are shown.For example,M is P-projective if and only if Ext1R (M,K) =0 for every finite generated K,if and only if Ext1R (M,R/I) =0 for any idea I of the ring R.Then the semisimple ring is charactered by P-projective modules andf-injective modules.For instance,R is semisimple if and only if every R-module is P-projective if and only if every R-module isf-injective.Finally,in order to discuss the properties of the submoudules of P-projective modules,the definition of the P-hereditary ring is described.It is proved that R is P-hereditary if and only if the injective dimension of the finitely generated module is less than 1.关键词
P-投射模/C-内射模/f-内射模/半单环/P-遗传环Key words
P-projective modules/C-injective modules/f-injective modules/ semisimple rings/ P-hereditary rings分类
数理科学引用本文复制引用
徐龙玉,王芳贵,陈翰林..P-投射模的刻画[J].四川师范大学学报（自然科学版）,2013,36(4):500-503,4.基金项目
国家自然科学基金(11171240)资助项目 （11171240）
