Complemented Elements In Ternarysemirings

Since we introduced the term complemented element in a Ternarysemiring and it is proved that (1) if p, q ∈ U such that p ⊲ q, then ppq = pqp = qpp = pp1. Further, if U is simple ⇒ p + q = q. (2) If U is a zero sum free Ternarysemiring and if l, g, h ∈ comp(U) then, (i) lgl⊥gl = 0 (ii) llg and l ⊏ g ∈ comp(U) (iii) llg = lgl = gll. (3) Let U be the zero sum free, then (i) If l, h ∈ comp(U) then l + h ∈ comp(U); (ii) 1+ 1 ∈ comp(U); (iii) comp(U) ⊆ I + (U) ; (iv) (comp(U) , + , [ ]) is a ternary sub semi ring of U are equivalent. Mathematics Sublect Classification: 16Y30, 16Y99