A study on (fuzzy) quasi-Gamma-hyperideals in ordered Gamma-semihypergroups

摘要

In this paper, as a generalization of the concept of quasi-Gamma-hyperideals of Gamma-semihypergroups to ordered Gamma-semihypergroup theory, the concept of quasi-Gamma-hyperideals of ordered Gamma-semihypergroups is introduced, and related properties are discussed. Furthermore, we define and study fuzzy quasi-Gamma-hyperideals of ordered Gamma-semihypergroups. In particular, we investigate the structure of fuzzy quasi-Gamma-hyperideal generated by a fuzzy subset in an ordered Gamma-semihypergroup. In addition, we also introduce the concepts of completely prime, weakly completely prime and completely semiprime fuzzy quasi-Gamma-hyperideals of ordered Gamma-semihypergroups, and characterize bi-regular ordered Gamma-semihypergroups in terms of completely semiprime fuzzy quasi-Gamma-hyperideals. Finally, several characterizations of regular and intra-regular ordered Gamma-semihypergroups by the properties of fuzzy quasi-Gamma-hyperideals are given.