Factor-square-full半模  

Factor-square-full semimodules

作　　者：王永铎[1] 鲁靖 WANG Yong-duo;LU Jing(School of Science,Lanzhou Univ.of Tech.,Lanzhou 730050,China)

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《兰州理工大学学报》2023年第5期150-156,共7页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(11861043)。

摘　　要：作为factor-square-full模的真推广,引入了factor-square-full半模的概念.设S是半环,M是左S-半模.称M的真subtractive子半模X是d-square,若存在正规满同态f:M→(M/X)2;称M的真subtractive子半模X是quasi-d-square,若存在M的d-square子半模Y使得X≤Y;称M是factor-square-full,若M的任意真subtractive子半模是quasi-d-square.讨论了这些子半模类及factor-square-full半模的性质.As a proper generalization of factor-square-full modules,the concept of factor-square-full semimodules is introduced in this paper.Let S be a semiring and M a left S-semimodule.A proper subtractive subsemimodule X of M is said to be d-square if there exists a normal epimorphism f:M→(M/X)2;A proper subtractive subsemimodule X of M is said to be quasi-d-square if there exists a d-square subsemimodule Y such that X≤Y;M is said to factor-square-full if any proper subsemimodule is quasi-d-square.The properties of these subsemimodule classes and factor-square-full semimodules are discussed.

关 键 词：正规满同态 d-square子半模 quasi-d-square子半模 factor-square-full半模 

分 类 号：O152.7[理学—数学]