Том 71
№ 11

All Issues

Yurevych О. V.

Articles: 1
Article (Ukrainian)

Criteria for Invertibility of Elements in Associates

Yurevych О. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 11. - pp. 1556-1563

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.