Abstract
We continue the investigation of invertible elements in associates, i.e., in (n + 1)-ary groupoids that are (i, j)-associative for all i ≡ j (mod s), where s is a divisor of a number n. For s = 1, an arbitrary associate is a semigroup. We establish two new criteria for the invertibility of elements, which generalize the results obtained earlier, and formulate corollaries for (n + 1)-groups and polyagroups, i.e., quasigroup associates.
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Yurevych, O.V. Criteria for Invertibility of Elements in Associates. Ukrainian Mathematical Journal 53, 1895–1905 (2001). https://doi.org/10.1023/A:1015211115378
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DOI: https://doi.org/10.1023/A:1015211115378