Idempotent and Inverse Elements in Strong Ternary Semirings
نویسنده
چکیده
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 semirings 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 idempotent; E∗(S) is closed under the multiplication and so (S,+, .) is an orthodox ST-semiring. Mathematics Subject Classification: 15A09, 16A78, 20M07, 20M18
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تاریخ انتشار 2016