On quasi-hyperideals and bi-hyperideals in multiplicative hypersemirings

In this paper we introduce the notion of quasi-hyperideal in multiplicative hypersemirings which is a generalization of one-sided hyperideal and study some of its properties and obtain some characterizations of quasi-hyperideal in multiplicative hypersemirings. Also, we introduce the notion of bi-hyperideal in multiplicative hypersemirings. We prove that in a multiplicative hypersemiring every quasi-hyperideal is a bi-hyperideal, but the converse is not true. Lastly, we characterize regular multiplicative hypersemiring with the help of quasi-hyperideal and bi-hyperideal.

Keywords:

Multiplicative hypersemiring , minimal left hyperideal , minimal right hyperideal , quasi-hyperideal , bi-hyperideal , regular multiplicative hypersemiring