Minimal order semihypergroups of type U on the right, II

作者：Freni Domenico^*

来源：Journal of Algebra, 2011, 340(1): 77-89.

DOI：10.1016/j.jalgebra.2011.05.015

• Type U semihypergroups
• Hypergroups
• Fundamental relations

We prove a new characterization of the heart W-H and of the derived D-H of a finite semihypergroup H of type U on the right, in terms of its hyperproducts. Consequently, we characterize the minimal size of the proper semihypergroups H of type U on the right such that W-H = D-H not equal H, W-H not equal D-H not equal H, or W-H not equal D-H = H. More-over, we obtain new results on the fundamental relations beta and gamma on finite semihypergroups of type U on the right. In particular, we prove that gamma is transitive, beta is transitive if vertical bar H vertical bar <= 8, and that there exist semihypergroups of type U on the right of size >= 9 where beta is not transitive. Hence, the minimal size for a semihypergroup of type U on the right to have a nontransitive beta is 9.

• 出版日期2011-8-15