Criteria for Invertibility of Elements in Associates

  • О. V. Yurevych


We continue the investigation of invertible elements in associates, i.e., in (n + 1)-ary groupoids that are (i, j)-associative for all ij (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.
How to Cite
YurevychО. V. “Criteria for Invertibility of Elements in Associates”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 53, no. 11, Nov. 2001, pp. 1556-63,
Research articles