Commuting degree for BCK-algebras
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908335952887808 |
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| author | Evans, C. Matthew |
| author_facet | Evans, C. Matthew |
| contents | We discuss the following question: given a finite BCK-algebra, what is the probability that two randomly selected elements commute? We call this probability the \textit{commuting degree} of a BCK-algebra. In a previous paper, the author gave sharp upper and lower bounds for the commuting degree of a BCK-algebra with order $n$. We expand on those results in this paper: we show that, for each $n\geq 3$, there is a BCK-algebra of order $n$ realizing each possible commuting degree and that the minimum commuting degree is achieved by a unique BCK-algebra of order $n$ Additionally, we show that every rational number in $(0,1]$ is the commuting degree of some finite BCK-algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17283 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Commuting degree for BCK-algebras Evans, C. Matthew Rings and Algebras 06F35, 03B47 We discuss the following question: given a finite BCK-algebra, what is the probability that two randomly selected elements commute? We call this probability the \textit{commuting degree} of a BCK-algebra. In a previous paper, the author gave sharp upper and lower bounds for the commuting degree of a BCK-algebra with order $n$. We expand on those results in this paper: we show that, for each $n\geq 3$, there is a BCK-algebra of order $n$ realizing each possible commuting degree and that the minimum commuting degree is achieved by a unique BCK-algebra of order $n$ Additionally, we show that every rational number in $(0,1]$ is the commuting degree of some finite BCK-algebra. |
| title | Commuting degree for BCK-algebras |
| topic | Rings and Algebras 06F35, 03B47 |
| url | https://arxiv.org/abs/2504.17283 |