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<p>Let <i>S</i> be a monoid. We define fuzzy independent subsets of fuzzy <i>S</i>-acts and use them to characterize the fuzzy basis of fuzzy <i>S</i>-acts. Furthermore, we prove that a fuzzy <i>S</i>-act is a free object in category of fuzzy <i>S</i>-acts if and only if it possesses a fuzzy basis. Additionally, we investigate the conditions under which a free fuzzy <i>S</i>-act is projective.</p>

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Free objects in the category of fuzzy S-acts

  • 期刊论文

  • 发表日期：

    2025年12月15日

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  • Pingting Ma,
  • Husheng Qiao

摘要

Let S be a monoid. We define fuzzy independent subsets of fuzzy S-acts and use them to characterize the fuzzy basis of fuzzy S-acts. Furthermore, we prove that a fuzzy S-act is a free object in category of fuzzy S-acts if and only if it possesses a fuzzy basis. Additionally, we investigate the conditions under which a free fuzzy S-act is projective.