形式三角矩阵环上的广义内射模

摘要

Let T be a formal triangular matrix ring, U and V be right T-modules, we introduced a concept of f-simple relative injectivity, N-generated relative injectivity and weakly simple relative injec-tivity of modules over T, and studied the f-relative injective, N-generated relative injective and weakly relative injective by means of the category Ω being equivalent to Mod-T. For right T-modules U and V, some sufficient conditions were obtained for U to be f-V-injective, N-generated V-injective or weakly V-injective.%设T是形式三角矩阵环,U和V是右T-模.引入f-单相对内射模、N-生成相对内射模和弱单相对内射模的概念,并借助于与Mod-T等价的范畴Ω,研究了形式三角矩阵环T上的f-相对内射模、N-生成相对内射模和弱相对内射模的有关性质.对右T-模U和V,得到U是f-V-内射模、N-生成V-内射模和弱V-内射模的充分条件.