JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (5): 5-8.doi: 10.6040/j.issn.1671-9352.0.2023.510

• Group Theory • Previous Articles    

Monoids over which all flat S-acts satisfy condition(E)

QIAO Husheng1,2, LIU Yuanjun1,2   

  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:2025-05-19

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Abstract: Let S be a monoid. The characterization of monoids for which all flat-acts satisfy condition(E)is studied. Under certain conditions, it is proved that all flat S-acts satisfy condition(E)if and only if S is a monoid formed by adding an identity element to a left zero semigroup, or S is a trivial monoid. The existing results are generalized.

Key words: left S-act, flatness, condition(E), condition(P)

CLC Number: 

  • O152
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