| 形式三角矩阵环上的广义内射模(英文) |
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| 引用本文： | 范维丽,刘仲奎.形式三角矩阵环上的广义内射模(英文)[J].兰州大学学报(自然科学版),2009,45(4). |
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| 作者姓名： | 范维丽 刘仲奎 |
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| 作者单位： | 1. 北京工业大学,应用数理学院,北京,100124
2. 西北师范大学,校长办公室,兰州,730070 |
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| 基金项目： | Supported by the National Natural Science Foundation of China(10671061);;the Natural Science Foundationof Beijing(1092002) |
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| 摘 要： | 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.
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| 关 键 词： | 三角形式矩阵环 f-相对内射模 N-生成相对内射模 弱相对内射模 |
Generalized injective modules over formal triangular matrix rings |
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| FAN Wei-Li,LIU Zhong-kui.Generalized injective modules over formal triangular matrix rings[J].Journal of Lanzhou University(Natural Science),2009,45(4). |
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| Authors: | FAN Wei-Li LIU Zhong-kui |
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| Institution: | 1.College of Applied Sciences;Beijing University of Technology;Beijing 100124;China 2.Headmaster's Office;Northwest Normal University;Lanzhou 730070;China |
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| Abstract: | 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. |
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| Keywords: | formal triangular matrix ring f-relative injective module N-generated relative injectivemodule weakly relative injective module |
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