Pure ideals in ordered power semigroups on semihypergroups induced by posets (Q6543372)

I cite from the authors abstract and the final conclusion.\N\NOrdered power semigroups on semihypergroups induced by posets are algebraic structures which are generalization of power semigroups on semihypergroups. In this paper, we investigate properties of ideals and pure ideals in ordered power semigroups on semihypergroups induced by posets.\N\NBy using the concept of partial order on the ordered power set introduced by \textit{M. Szymanska} and \textit{D. Schweigert} [in: Discrete mathematics and applications. Proceedings of the 6th international conference, Bansko, Bulgaria, August 31--September 2, 2001. Blagoevgrad: South-West University. 71--76 (2002; Zbl 1014.06001)], we can construct the ordered power semigroups on semihypergroups induced by posets. This structure is a generalization of power semigroups. The concept of pure ideals can be applied to this structure and the properties of ideals and pure ideals of the structure are investigated in this paper.\N\NThe paper contains two nice concrete examples.