Criteria for Invertibility of Elements in Associates
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.
English version (Springer): Ukrainian Mathematical Journal 53 (2001), no. 11, pp 1895-1905.
Citation Example: Yurevych О. V. Criteria for Invertibility of Elements in Associates // Ukr. Mat. Zh. - 2001. - 53, № 11. - pp. 1556-1563.