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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2209.12088 |
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| _version_ | 1866914810545831936 |
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| author | Lipparini, Paolo |
| author_facet | Lipparini, Paolo |
| contents | We say that an idempotent term $t$ is an exact-$m$-majority term if $t$ evaluates to $a$, whenever the element $a$ occurs exactly $m$ times in the arguments of $t$, and all the other arguments are equal. If $m<n$ and some variety $\mathcal V$ has an $n$-ary exact-$m$-majority term, then $\mathcal V$ is congruence modular. For certain values of $n$ and $m$, for example, $n=5$ and $m=3$, the existence of an $n$-ary exact-$m$-majority term neither implies congruence distributivity, nor congruence permutability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_12088 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Exact-$m$-majority terms Lipparini, Paolo Rings and Algebras 08B05, 08B10 We say that an idempotent term $t$ is an exact-$m$-majority term if $t$ evaluates to $a$, whenever the element $a$ occurs exactly $m$ times in the arguments of $t$, and all the other arguments are equal. If $m<n$ and some variety $\mathcal V$ has an $n$-ary exact-$m$-majority term, then $\mathcal V$ is congruence modular. For certain values of $n$ and $m$, for example, $n=5$ and $m=3$, the existence of an $n$-ary exact-$m$-majority term neither implies congruence distributivity, nor congruence permutability. |
| title | Exact-$m$-majority terms |
| topic | Rings and Algebras 08B05, 08B10 |
| url | https://arxiv.org/abs/2209.12088 |