JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (8): 1-8.doi: 10.6040/j.issn.1671-9352.0.2023.362

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A note on fractional S-acts

Xingliang LIANG1,2(),Yuhang LI1   

  1. 1. School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi'an 710021, Shaanxi, China
    2. School of Mathematics, Northwest University, Xi'an 710127, Shaanxi, China
  • Received:2023-08-23 Online:2024-08-20 Published:2024-07-31

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Abstract:

Let S be a commutative monoid, in the category of S-acts, by the injectivity and surjectivity of the mapping of pullback diagrams, a new proof that fractional functors (the category of S-acts to the category of fractional S-acts) preserve flatness properties is given. The relationship between fractional functors and directed colimits is investigated. A sufficient condition for fractional S-acts having a cover is presented.

Key words: commutative monoids, S-acts, pullback diagrams, flatness properties, directed colimits

CLC Number: 

  • O152.7

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