Idempotent and inverse elements in strong ternary semirings
Rabah Kellil · International Mathematical Forum · 2016
In continuation of a previous works on semirings (5), in the present paper we introduce the notions of a strong ternary semiring (ST-semiring) (that is a ternary semirings with an additional condition called the left invertive law). We prove that many results obtained in (5) for semir- ings are still valid in the present case. We establish some relationships between the idempotents for both the addition and the multiplication. We prove in the case of ST-semiring, that the set of multiplicative idem- potent; E (S) is closed under the multiplication and so (S; +;:) is an orthodox ST-semiring. Mathematics Subject Classication: 15A09, 16A78, 20M07, 20M18