Nilpotent BCK-algebras
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912784144400384 |
|---|---|
| author | Evans, C. Matthew |
| author_facet | Evans, C. Matthew |
| contents | We recall the derived subalgebra of a BCK-algebra, and use this to define the derived ideal. Using the derived ideal, we show that the category of commutative BCK-algebras is a reflective subcategory of the category of BCK-algebras. After this, we introduce central series and define a notion of nilpotence for BCK-algebras and prove some properties of nilpotence. In particular, for any variety of BCK-algebras, the sub-class of nilpotent algebras is a sub-pseudovariety, though in general not a variety. We also show that the class of BCK-algebras of nilpotence class at most $c$ is a sub-quasivariety of all BCK-algebras, and is a variety if and only if $c=1$. We close by showing that every finite BCK-algebra is nilpotent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08976 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nilpotent BCK-algebras Evans, C. Matthew Rings and Algebras 06F35, 20F19, 03G99 We recall the derived subalgebra of a BCK-algebra, and use this to define the derived ideal. Using the derived ideal, we show that the category of commutative BCK-algebras is a reflective subcategory of the category of BCK-algebras. After this, we introduce central series and define a notion of nilpotence for BCK-algebras and prove some properties of nilpotence. In particular, for any variety of BCK-algebras, the sub-class of nilpotent algebras is a sub-pseudovariety, though in general not a variety. We also show that the class of BCK-algebras of nilpotence class at most $c$ is a sub-quasivariety of all BCK-algebras, and is a variety if and only if $c=1$. We close by showing that every finite BCK-algebra is nilpotent. |
| title | Nilpotent BCK-algebras |
| topic | Rings and Algebras 06F35, 20F19, 03G99 |
| url | https://arxiv.org/abs/2507.08976 |