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 V has an n-ary exact-m-majority term, then 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.
Lipparini, P. (2024). Exact-m-majority terms. MATHEMATICA SLOVACA, 74(2), 293-298 [10.1515/ms-2024-0022].
Exact-m-majority terms
Lipparini, Paolo
2024-01-01
Abstract
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 V has an n-ary exact-m-majority term, then 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.File in questo prodotto:
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