(m,n)-内射环的推广

将(m,n)-内射环的概念推广到(J,K)-(m,n)-内射环,给出(J,K)-(m,n)-内射环的等价刻划.并借助(m,n)-内射环的某些性质研究(J,K)-(m,n)-内射环.

(I,K)-(m,n)-内射环

引入了(I,K)-(m,n)-内射环的概念,给出了(I,K)-(m,n)-内射环的等价刻划.讨论了(I,K)-(m,n)-内射环与(I,K)-(m,1)-内射环之间的关系及左(I,K)-(m,n)-内射环和右(I,K)-(m,n)-内射环的关系.证明了R是右(I,K)-(m,n)-内射环当且仅当如果z=(m1,m2,…,mn)∈Kn且A∈Im×n,rRn(A)rRn(z),则存在y∈Km,使得z=yA.推广了已知的相关结论.

(m,n)-内射环的一个特征

用闭子模刻画了右 (m ,n) -内射环并证明了环R为右 (m ,n) -内射的当且仅当n-生成的投射左R-模的m -生成子模为闭子模 .

Some Relations on Generalizations of Injective Rings

Some relations about the generalizations of self-injective ring: P-injective ring, GP-injective ring, AP-injective ring, simple-injective ring and n-injective ring are studied.