摘要
文中引入强左(m,n)-凝聚环R(如果左R-模Rm的每个n-生成子模是(m,n)-表现),证明了在强(m,n)-凝聚环上,(P(m,n),I(m,n))和(F(m,n),C(m,n))是遗传余挠理论;每个左R-模是(m,n)-投射当且仅当每个(m,n)-内射左R-模是(m,n)-投射当且仅当每个(m,n)-内射左R-模存在有唯一映射性质的P(m,n)-覆盖。
A ring R is called strongly left (m,n)-coherent if every n-generated submodule of Rm is (m,n)-presented.Suppose that a ring R is strongly left (m,n)-coherent.Then (P(m,n),I(m,n)) and (F(m,n),C(m,n)) are hereditary cotorsion theory,each left R-module is (m,n)-projective if and only if each (m,n)-injective left R-module is (m,n)-projective if and only if each (m,n)-injective left R-module has a P(m,n)-cover with unique mapping property.
出处
《江南大学学报(自然科学版)》
CAS
2014年第5期611-615,共5页
Joural of Jiangnan University (Natural Science Edition)
基金
国家自然科学基金项目(11201063)
福建省科技厅基金项目(2013J05013)
福建省教育厅项目(JA11209)
莆田学院教改项目(JG201316)