JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (11): 1-5.doi: 10.6040/j.issn.1671-9352.0.2023.499

• Algebraic Structures •    

Some studies on condition(IE)

QIAO Husheng1,2, ZHANG Xueqian1*   

  1. 1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China;
    2. Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics, Lanzhou 730070, Gansu, China
  • Published:2025-11-11

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Abstract: Let S be a monoid, and K be a right ideal of S. A generalized condition(IE)of condition(E)is introduced. The relationship between condition(IE)and condition(E)and other flat properties is studied. The coproduct, amalgamated coproduct and direct product of S-acts satisfying condition(IE)are discussed. In addition, the necessary and sufficient conditions for the cyclic acts S/ρ, diagonal acts D(S) and Rees quotient acts S/K to satisfy condition(IE)are given.

Key words: monoid, S-act, condition(E), condition(IE)

CLC Number: 

  • O152.7
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