Criteria for Invertibility of Elements in Associates

Authors

  • О. V. Yurevych

Abstract

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.

Published

25.11.2001

Issue

Section

Research articles

How to Cite

Yurevych О. V. “Criteria for Invertibility of Elements in Associates”. Ukrains’kyi Matematychnyi Zhurnal, vol. 53, no. 11, Nov. 2001, pp. 1556-63, https://umj.imath.kiev.ua/index.php/umj/article/view/4375.