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<p>In this paper, we introduce the notion of abelian quotients in groupoids, and we discuss some entropy of commutativity of several groupoids defined on the set of all natural numbers. We characterize linear groupoids having the same abelian quotients. Moreover, we apply this notion to the associative law in groupoids.</p>

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Abelian quotients in groupoids

  • 期刊论文

  • 发表日期：

    2025年5月6日

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  • Hee Sik Kim,
  • Sun Shin Ahn,
  • Choonkil Park

摘要

In this paper, we introduce the notion of abelian quotients in groupoids, and we discuss some entropy of commutativity of several groupoids defined on the set of all natural numbers. We characterize linear groupoids having the same abelian quotients. Moreover, we apply this notion to the associative law in groupoids.