A Simple Study on the Structures of Zeroid and Ordered SemiringsJournal: International Research Journal of Advanced Engineering and Science (IRJAES) (Vol.1, No. 4)
Publication Date: 2016-10-09
Authors : N. Sulochana; M. Amala; Y. Monikarchana;
Page : 26-28
Keywords : Band; K-regular semiring; maximum; positive totally ordered.;
In this paper we have proved that Suppose S is a semiring in which (S, +) be zeroid then a + ab + b = 2b in the following cases. (i) If (S, ?) is right singular semigroup and (ii) If (S, ?) is a band. Also we have established that If S is a totally ordered semiring with multiplicative identity 1 and (S, ?) is p.t.o, then (S, +) is non-negatively ordered.
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