Journal of Lanzhou University of Technology ›› 2023, Vol. 49 ›› Issue (5): 150-156.

• Scientific • Previous Articles     Next Articles

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

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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