兰州理工大学学报

兰州理工大学学报 ›› 2023, Vol. 49 ›› Issue (5): 150-156.

• 数理科学 • 上一篇    下一篇

Factor-square-full半模

王永铎*, 鲁靖   

  1. 兰州理工大学 理学院, 甘肃 兰州 730050
  • 收稿日期:2022-04-24 出版日期:2023-10-28 发布日期:2023-11-07
  • 通讯作者: 王永铎(1974-),男,甘肃靖远人,博士,教授. Email:ydwang@lut.edu.cn
  • 基金资助:
    国家自然科学基金(11861043)

Factor-square-full semimodules

WANG Yong-duo, LU Jing   

  1. School of Science, Lanzhou Univ. of Tech., Lanzhou 730050, China
  • Received:2022-04-24 Online:2023-10-28 Published:2023-11-07

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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.

关键词: 正规满同态, d-square 子半模, quasi-d-square 子半模, factor-square-full半模

Abstract: 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.

Key words: normal epimorphism, d-square subsemimodules, quasi-d-square subsemimodules, factor-square-full semimodules

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