Semipseudo Symmetric Ideals in Partially Ordered Ternary Semigroups

Abstract

 In this paper the terms pseudo symmetric ideals, semipseudo symmetric ideals of po ternary semigroups.  It is proved that every pseudo symmetric ideal of po ternary semigroup is a semipseudo symmetric ideal.  It is also proved that every semiprime ideal P minimal relative to containing a semipseudo symmetric ideal A of a po ternary semigroup is completely semiprime.  If  A is a semipseudo symmetric ideal of a po ternary semigroup T.  Then (1) A₁₌ the intersection of all completely prime ideals of T containing A. 2)   = the intersection of all minimal completely prime ideals of T containing A.  3) = the minimal completely semiprime ideal of T relative to containing A.4) for some odd natural number n}5)  = the intersection of all prime ideals of T containing A.6) = the intersection of all minimal prime ideals of T containing A.7)  = the minimal semiprime ideals of relative to containing A.8)  for some odd natural number n } are equivalent.  If A is an ideal in a po ternary semigroup then it is proved that (1) A is completely semiprime, A is semiprime and pseudo symmetric. A is semiprime and semipseudo symmetric are equivalent and (2) A is completely prime; A is prime and pseudo symmetric.  A is prime and semipseudo symmetric are also equivalent.  If M is maximal ideal of a po ternary semigroup T with then it is proved that M is completely prime, M is completely semiprime, M is pseudo symmetric and M is semipseudo symmetric are equivalent.