Characterizations of Regular Ordered Semirings by Ordered Quasi-Ideals

الملخص EN

We introduce the notion of an ordered quasi-ideal of an ordered semiring and show that ordered quasi-ideals and ordered bi-ideals coincide in regular ordered semirings.

Then we give characterizations of regular ordered semirings, regular ordered duo-semirings, and left (right) regular ordered semirings by their ordered quasi-ideals.